Advancements in thermoelectric materials: optimization strategies for enhancing energy conversion

Haiwei Han; Lijun Zhao; Xinmeng Wu; Bin Zuo; Shunuo Bian; Tao Li; Xinyue Liu; Yaohong Jiang; Chunyan Chen; Jiali Bi; Junhua Xu; Lihua Yu

doi:10.1039/D4TA03666B

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DOI: 10.1039/D4TA03666B (Review Article) J. Mater. Chem. A, 2024, Advance Article

Advancements in thermoelectric materials: optimization strategies for enhancing energy conversion

Haiwei Han , Lijun Zhao *, Xinmeng Wu , Bin Zuo , Shunuo Bian, Tao Li, Xinyue Liu, Yaohong Jiang, Chunyan Chen, Jiali Bi, Junhua Xu * and Lihua Yu *
School of Material and Science, Jiangsu University of Science and Technology, Zhenjiang 212000, China. E-mail: ljzhao@just.edu.cn; jhxu@just.edu.cn; lhyu6@just.edu.cn

Received 27th May 2024 , Accepted 12th August 2024

First published on 23rd August 2024

Abstract

Thermoelectric materials are a highly promising category of energy conversion materials. In this paper, we present a multitude of approaches to enhance the efficacy of these materials. The review begins with an introduction to the fundamental concept of the thermoelectric figure of merit (ZT), a key parameter for assessing the performance of thermoelectric materials, as well as theories of electrical and thermal transport, which lay the groundwork for understanding and improving the performance of thermoelectric materials. Subsequently, this paper delves into several typical optimization strategies, including the enhancement of material performance through low-dimensionalization and quantum confinement effects, with detailed discussions on two-dimensional, one-dimensional, and zero-dimensional materials. The role of point defect engineering in modulating material properties and the significance of nano-composite materials in enhancing thermoelectric performance are also explored. Band engineering, an effective optimization technique, offers multiple possibilities for enhancing thermoelectric performance through the adjustment of carrier effective mass, utilization of resonance states, band degeneracy, band convergence, and bandgap tuning. Additionally, the application of phonon engineering in reducing thermal conductivity and improving thermoelectric conversion efficiency is highlighted. Discussions on special structures such as textures, single crystals, core–shell structures, and porous structures, as well as symmetry control strategies, highlight the importance of microstructural control in optimizing thermal conductivity. Consequently, the review explores the significance of the synergistic effects of different strategies, noting that an integrated application of these strategies can maximize the performance of thermoelectric materials. The use of materials genomics and machine learning in screening highly potential thermoelectric materials is also highlighted. Finally, the paper addresses the challenges and developments related to the stability, scalability, sustainability, and integration of thermoelectric materials with other systems. Overall, this article summarizes a series of optimization strategies for thermoelectric materials, providing valuable references and inspiration for researchers in the field, with the aim of further advancing the science of thermoelectric materials.

Haiwei Han

Haiwei Han graduated from Harbin University of Science and Technology in 2018 with a bachelor's degree. He is currently pursuing a master's degree at the School of Materials Science and Engineering, Jiangsu University of Science and Technology. His current research interests focus on thermoelectric materials and two-dimensional materials.

Lijun Zhao

Dr Lijun Zhao is currently a research associate in School of Materials Science and Engineering at Jiangsu University of Science and Technology. He received his PhD degree from Jiangsu University in 2021. He mainly focuses on the development of high-performance bulk Cu₃SbSe₄-based thermoelectric materials.

Xinmeng Wu

Xinmeng Wu is currently a PhD candidate in the School of Materials and Science Engineering in Jiangsu University of Science and Technology. He received his B.S. (2010–2014) from Jiangsu University of Science and Technology and got his M.S. (2014–2017) from Shanghai Institute of Technology. His current research interests focus on the design, preparation, and characterization of the film materials and composite materials.

Bin Zuo

Dr Zuo Bin is an associate professor at Jilin Normal University, graduated with a PhD from the School of Materials Science and Engineering at Jiangsu University of Science and Technology in 2024. She is engaged in the research of the microstructure, mechanical properties, and tribological performance of film materials, as well as the properties of Fe-based alloys.

Junhua Xu

Prof. Junhua Xu is a professor in School of Materials Science and Engineering, Jiangsu University of Science and Technology, China. He received his B.S. degree (1985) in Materials Science and Engineering, M.S. degree in Materials Science (1989) from Jiangsu University, and PhD degree in Materials Science (2000) from Shanghai Jiaotong University. He was a postdoctoral Special Research fellow at the University of Tokyo (2000–2002) and the National Institute of Industrial Technology, Japan, (2002–2004). His main research directions are the preparation, microstructure, mechanical properties, friction and wear properties of films, and the joining technology.

Lihua Yu

Prof. Lihua Yu is a professor in School of Materials Science and Engineering, Jiangsu University of Science and Technology, China. She received his B.S. degree (1985) in Materials Science and Engineering and M.S. degree in Materials Science (1996) from Jiangsu University. Her main research directions are the preparation, microstructure, mechanical properties, friction and wear properties of nanostructured multilayer films and composite films, and the joining technology of spray-formed aluminum alloy.

1 Introduction

Thermoelectric (TE) materials can convert thermal energy into electrical energy and vice versa. This solid-state, vibration-free technology has long been used to power spacecraft in several of NASA's deep space missions. In recent decades, energy crises and environmental issues have become the focus of public attention and research. Thermoelectric materials, as a new type of energy conversion material, are expected to be an effective solution to these problems.^1,2 Although there are many types of thermoelectric materials with a wide range of applications, their low energy conversion efficiency has been one of the main obstacles to large-scale production and application. The energy conversion efficiency of thermoelectric materials is directly related to the dimensionless figure of merit ZT. In theory, the higher the thermoelectric figure of merit ZT, the higher the thermoelectric conversion efficiency, which can approach the Carnot cycle limit.³ The formula for ZT is given by: ZT = (S²σT)/(κ_e + κ_l + κ_b),⁴ where S is the Seebeck coefficient, σ is the electrical conductivity, κ represents thermal conductivity, T is the absolute temperature, κ_e is the electronic thermal conductivity, and κ_l is the lattice thermal conductivity, κ_b is the bipolar diffusion thermal conductivity.^5,6 Generally, these parameters are interdependent, making it challenging to independently tune any single parameter. Increasing S usually means reducing the carrier concentration, which can lead to a decrease in electrical conductivity σ, thus requiring a balance between the two. Additionally, the thermal conductivity κ consists of three components: electronic thermal conductivity κ_e, lattice thermal conductivity κ_l, and bipolar diffusion thermal conductivity κ_b. Reducing lattice thermal conductivity is typically achieved by introducing crystal defects or interface scattering, which may impact the electronic transport properties. Consequently, optimization strategies for thermoelectric materials must rigorously account for the interdependencies between electrical conductivity, Seebeck coefficient, and thermal conductivity to enhance overall performance.

In this review, we systematically summarize and introduce common optimization strategies for thermoelectric materials based on thermoelectric transport theory. These strategies include dimensional reduction, point defect engineering, nanocomposites, band engineering, phonon engineering, and special structures, and their applications in improving thermoelectric material performance. We also discuss how these methods can achieve independent or synergistic regulation of electronic and thermal transport properties. Through the introduction of these strategies, this review aims to provide a comprehensive and in-depth reference framework for thermoelectric researchers, aiding in the innovation and development of future thermoelectric materials.

In conclusion, this review will address prevailing challenges and delineate prospective development trajectories in thermoelectric material research. Particular emphasis will be placed on advanced topics such as material genome engineering and the Materials Genome Initiative, which represent critical and visionary challenges within the thermoelectric materials research domain.

The Seebeck effect marks the inception of thermoelectricity development.⁷ When two different conductive materials (such as A and B) are joined together and the temperature at the two junctions differs, an electric current is generated in the circuit driven by the temperature difference, creating a potential difference V_ab across the materials. Fig. 1 presents a simplified schematic representation of the Seebeck effect. When the temperature difference ΔT at the two conductive junctions is very small, the Seebeck coefficient can be defined as follows:


	(1)


	Fig. 1 Thermoelectric effects: schematic diagrams of the Seebeck effect.

The international unit for the Seebeck coefficient is V K⁻¹, commonly expressed in μV K⁻¹.

In 1834, the French physicist Peltier discovered the Peltier effect, which is the inverse of the Seebeck effect.⁸ The Peltier effect can be utilized for solid-state refrigeration. Fig. 2 presents a simplified schematic representation of the Peltier effect. In 1854, Thomson discovered the Thomson effect,⁹ marking the robust growth of thermoelectrics since then. Fig. 3 depicts a schematic of the Thomson effect.


	Fig. 2 Thermoelectric effects: schematic diagrams of the Peltier effect.


	Fig. 3 Thermoelectric effects: schematic diagrams of the Thomson effect.

The ultimate application of thermoelectric materials lies in thermoelectric devices. The most critical parameter for characterizing the performance of thermoelectric devices is the thermoelectric conversion efficiency, which encompasses both power generation and cooling efficiency. The maximum power generation efficiency (η_g,max) and the cooling efficiency parameter COP (Coefficient of Performance) of thermoelectric devices depend on the material's cold-side temperature, hot-side temperature, and the thermoelectric figure of merit. The values of η_g,max and COP are both given as:¹⁰


	(2)


	(3)

where, T_h represents the hot-end temperature, T_c is the cold-end temperature, and

, where

is the average operating temperature. Z is the material's quality factor, with the dimension of K⁻¹. As indicated by the above formulae (2) and (3), for the maximum power generation efficiency η_g,max and the cooling efficiency parameter COP of a thermoelectric device, the higher the dimensionless thermoelectric figure of merit ZT, the higher the power generation and cooling efficiencies. In 1911, Altenkirch³ derived the expression for the thermoelectric figure of merit ZT, which measures the performance of thermoelectric materials:⁴


	(4)

where, S represents the Seebeck coefficient of the material, commonly measured in microvolts per Kelvin (μV K⁻¹); σ is the material's electrical conductivity, typically expressed in Siemens per meter (S m⁻¹); κ denotes the thermal conductivity of the material, with the usual unit being Watts per meter-Kelvin (W m⁻¹ K⁻¹); and T is the absolute temperature, measured in Kelvin (K). The thermal performance of the materials are characterized by the thermal conductivity, κ, which includes three components: electronic thermal conductivity, κ_e, lattice thermal conductivity, κ_l, and bipolar diffusion thermal conductivity, κ_b. To achieve thermoelectric materials with superior performance, it is necessary to increase the electrical conductivity and Seebeck coefficient, while simultaneously reducing the thermal conductivity. Fig. 4 illustrates the development history of thermoelectric theory.


	Fig. 4 The historical development of thermoelectric theory.

1.1 Electrical transport theory

Most thermoelectric materials fall into the category of semiconductor materials, where electrical transport primarily depends on the characteristics of carrier transport. The main parameters influencing electrical conductivity and the Seebeck coefficient are the carrier concentration, carrier mobility, and carrier scattering.

1.1.1 Electrical conductivity. For most thermoelectric materials, their electrical transport properties can be described by solving the Single Parabolic Band model (abbreviated as SPB model).^11,12 For semiconductor materials, the electrical conductivity (σ) can be expressed as:


	(5)


	(6)

where, K_B represents the Boltzmann constant, η is the reduced Fermi level, r is the scattering factor, ℏ is the reduced Planck constant, m* is the effective mass of the carrier, n is the carrier concentration, μ is the carrier mobility, and e is the charge of an electron. The variable i can take on integer or half-integer values. As can be inferred from eqn (5) and (6), an increase in carrier concentration and carrier mobility does not necessarily occur simultaneously. In practical semiconductor thermoelectric materials, point defects, dislocations, grain boundaries, impurity phases, and other factors can scatter carriers, with different scattering mechanisms corresponding to different values of the scattering factor.

1.1.2 Seebeck coefficient. The Seebeck coefficient of thermoelectric materials is generally influenced by phonon drag effect and carrier thermal diffusion.¹³ In practical thermoelectric devices that generate electricity from a temperature difference, the impact of carrier thermal diffusion on the Seebeck coefficient is typically the primary consideration. For non-degenerate semiconductors, the Seebeck coefficient can be expressed as:


	(7)

For degenerate semiconductor of thermoelectric materials, the Seebeck coefficient can be represented as:


	(8)

From eqn (7) and (8), Seebeck coefficient is related to the effective mass of the carriers, the carrier concentration, the scattering factor, and the Fermi energy level.

We define the power factor (PF) of thermoelectric materials as the product of the square of the Seebeck coefficient (S) and the electrical conductivity (σ), namely PF = S²σ. The power factor is indicative of the material's electrical transport efficiency.

1.2 Thermal transport theory

Thermal conduction is the primary mode of heat transfer in solid materials, fundamentally resulting from the collisions and energy transfer among microscopic particles within the material. The total thermal conductivity κ can be expressed in eqn (9):


κ = κ_e + κ_l + κ_b	(9)

where, κ_e is the carrier thermal conductivity, κ_l is lattice thermal conductivity, and κ_b is bipolar diffusion thermal conductivity.

1.2.1 Carrier thermal conductivity. Carrier thermal conductivity in a crystal arises from the directed movement of carriers within the material. According to the Wiedemann–Franz Law, the carrier thermal conductivity can be determined as follows:


κ_e = LTσ	(10)

For non-degenerate semiconductors, the Lorenz number (L) can be calculated using the following formula:


	(11)

From the above equation, it is evident that the Lorenz number is influenced by the scattering factor r. The scattering factor depends on the carrier scattering mechanism, hence the Lorenz number for non-degenerate semiconductors will vary under different scattering mechanisms.

As for degenerate semiconductor materials:


	(12)

The Lorenz number L is typically taken as 2.45 × 10⁻⁸ WΩ K⁻². For degenerate semiconductor materials, the Lorenz number is not influenced by the scattering mechanism.

1.2.2 Lattice thermal conductivity. During the process of lattice vibration energy transfer, the energy propagates diffusively due to collisions, rather than in a straight line. Lattice thermal conductivity is caused by phonon diffusion. According to the kinetic theory of heat conduction, lattice thermal conductivity can be expressed as follows:


	(13)

In this expression, C_V is the specific heat capacity per unit volume, V represents the phonon propagation velocity, and L is the mean free path of phonons. The specific heat capacity is an intrinsic property of the material, and the mean free path of phonons is related to the scattering mechanism. This implies that lattice thermal conductivity is solely associated with the transport process of phonons and is not directly related to electrical conductivity or the Seebeck coefficient. Therefore, it can be independently adjusted and controlled as a separate parameter.

According to the Debye model using the relaxation time approximation, the lattice thermal conductivity of thermoelectric materials is expressed as:^14,15


	(14)

where, θ_Dis the Debye temperature, τ is the relaxation time, and x = ħω/k_BT, ħ is the reduced Planck constant, and ω is the phonon frequency. Generally, phonon transport in thermoelectric materials is affected by various scattering mechanisms, such as point defects, lattice vibrations, and grain boundaries. Fig. 5 shows the relationship between phonon scattering and frequency for different scattering mechanisms, indicating that the relaxation time is determined by a combination of these scattering mechanisms:¹⁶


	(15)

where, τ_q is phonon relaxation time, the resistive scattering processes include grain boundary scattering (τ_B), point defect scattering (τ_PD), phonon–phonon Umklapp processes (τ_U), electron–phonon interaction (τ_e–p).


	Fig. 5 The relationship between phonon scattering and frequency under different mechanisms.¹⁶ Reproduced from ref. 16 with permission from Springer Nature, copyright (2016).

1.2.3 Bipolar diffusion thermal conductivity. The bipolar diffusion thermal conductivity (κ_b) is related to the electrical conductivities of electrons and holes (σ_P and σ_N), and their respective Seebeck coefficients (S_P and S_N), as shown in eqn (16):¹⁷


	(16)

Typically, bipolar diffusion occurs concurrently with intrinsic excitation, commonly seen in narrow-band and lightly doped semiconductors. The increase in thermal conductivity due to bipolar diffusion is significant. Additionally, the mixing of electrons and holes in conduction can lead to a reduction in the Seebeck coefficient. Therefore, high-performance thermoelectric materials generally aim to avoid the occurrence of bipolar diffusion.

2 Typical optimization strategies

Thermoelectric materials, after several decades of development, have achieved significant accomplishments. During this period, researchers have employed a variety of different strategies to profoundly optimize and enhance the performance of thermoelectric materials. Table 1 displays a selection of thermoelectric materials that have achieved excellent thermoelectric performance, along with related data. The following section will elaborate on these typical optimization strategies, including the utilization of low-dimensionality and quantum confinement effects, as well as point defect engineering to regulate the thermoelectric performance of materials. The role of nanocomposite materials in enhancing thermoelectric performance is also discussed. Additionally, band engineering is presented as an effective optimization strategy. It improves thermoelectric performance by adjusting carrier effective mass, resonance states, band degeneracy, as well as band convergence and gap tuning. Moreover, the application of phonon engineering has also shown immense potential in reducing thermal conductivity and enhancing thermoelectric conversion efficiency. Special structures such as textures, single crystals, core–shell structures, and porous structures demonstrate the importance of controlling microstructures to optimize the performance of thermoelectric materials.

Table 1 Summary of ZT values for some excellent thermoelectric materials (ZT_max > 2)^a

Material	Crystalline	Type	ZT_max	T	Strategy	Ref
a PC-polycrystal; RT-room temperature; abbreviations for strategies: DR-dimensionality reduction; PD-point defects; N-nanocomposites; B-band engineering; P-phonon engineering; U-unique structures.
SnSe	PC	P	3.10	783	PD + P	18
Cu₂Se–BiCuSeO-graphene	PC	P	2.82	1000	N + P	19
SnSe_0.97Br_0.03	PC	N	2.80	773	PD + B	20
Ge_0.87Y_0.02Sb_0.10Ag_0.01	PC	P	2.70	323–773	PD + P + B + N	21
Cu_1.94Al_0.02Se	PC	P	2.62	1029	PD + P + B	22
SnSe	PC	P	2.60	923	PD + B	23
Cu₂Se + 1 mol% In	PC	P	2.60	850	PD + P + N + B	24
Pb_0.92Na_0.03Eu_0.03Sn_0.02Te	PC	P	2.51	823	PD + P + B	25
Pb_0.98Na_0.02Te + 8% SrTe	PC	P	2.50	923	PD + P + N + B	26
(Sn_0.95Pb_0.05)_0.99Na_0.01Se	PC	P	2.50	773	PD + P + N + U	27
Cu₂Se + 0.15 wt% graphene	PC	P	2.44	870	P + N	28
SnSe_0.97Br_0.03 + 12% PbSe	PC	N	2.40	723	PD + N + B	29
Ge_0.95Bi_0.05Te_1.025	PC	P	2.40	773	PD + P + B	30
Ge_0.86Pb_0.1B_0.04Te	PC	P	2.40	600	PD + P + B	31
Cu₂Se + 0.75 wt% CNTs	PC	P	2.40	1000	P + N	32
(GeTe)₁₇Sb₂Te₃	PC	P	2.40	773	PD + P + B	33
Ge_0.9Sb_0.1Te	PC	P	2.35	800	PD + P	34
Sn_0.97Na_0.03Se_0.9S_0.1	PC	P	2.30	773	PD + B	35
PbTe_0.85Se_0.15 + 2% Na + 4% SrTe	PC	P	2.30	923	PD + P + N + B	36
Ge_0.89Sb_0.1In_0.1Te	PC	P	2.30	650	PD + P + N + B	37
Ge_0.76Sb_0.08Pb_0.12Te	PC	P	2.30	800	PD + P + N	38
(PbTe)_0.7(PbS_)0.3 + 3% Na	PC	P	2.30	923	PD + P + N	39
Ge_0.87Pb_0.13Te	PC	P	2.25	673	PD + P + N + B	40
(GeTe)_0.937(Bi₂Se_0.2Te_2.8)_0.063	PC	P	2.25	723	PD + P + B	41
(GeTe)_0.73(PbSe)_0.27	PC	P	2.25	800	PD + P + N + B	42
(Ge_0.098Re_0.012Te)₁₂Sb₂Te₃	PC	P	2.25	773	PD + P + N + B	43
PbTe_0.7S_0.3 + 2.5% K	PC	P	2.24	823	PD + P + N	44
Cu₂Se + 0.1 wt% carbon-coated boron	PC	P	2.23	1000	P + N	45
Ge_0.89Cr_0.03Sb_0.08Te	PC	P	2.20	780	PD + P + N	46
Sn_0.98Pb_0.01Zn_0.01Se	PC	P	2.20	873	PD + P + N	47
Sn_0.985Na_0.015Se + 2% SnSe₂	PC	P	2.20	773	PD + N + B	48
Sn_0.94Bi_0.06Se	PC	N	2.20	773	PD + B	49
PbTe_0.8Se_0.02 + 8% MgTe	PC	P	2.20	820	PD + P + N	50
Pb_0.945Na_0.025Eu_0.03Te	PC	P	2.20	850	PD + P + N	51
Ge_0.9Cd_0.05Bi_0.05Te	PC	P	2.20	650	PD + P + B	52
Ge_0.93Bi_0.07Te_0.1005I_0.03	PC	P	2.20	723	PD + P + N + B	53
Ge_0.89Ti_0.03Sb_0.08Te	PC	P	2.20	725	PD + P + B	54
(GeTe)₁₇Sb₂Te₃+ 1.5% Bil₃	PC	P	2.20	723	PD + P + N + B	55
Ge_0.93Bi_0.03Pb_0.04Te	PC	P	2.14	670	PD	56
Cu_1.98Li_0.02Se	PC	P	2.14	973	PD + P + U + B	57
SnSe_0.95 + 3% PbBr₂	PC	N	2.10	770	PD + B	58
Sn_0.98Na_0.02Se_0.98Te_0.02	PC	P	2.10	793	PD + B	59
Sn_0.97Ge_0.03Se	PC	P	2.10	873	PD + P + N	60
Sn_0.95Se	PC	P	2.10	873	PD + P + B	61
Nano-Cu₂Se	PC	P	2.10	973	P + N + U	62
Ge_0.9Sb_0.1Te_0.9Se_0.05S_0.05	PC	P	2.10	630	PD + P + N + B	63
Ge_0.94Bi_0.06Te + 0.2% nano-SiC	PC	P	2.10	723	PD + P + N + B	64
Ge_0.93In_0.01Bi_0.06Te	PC	P	2.10	723	PD + P + B	65
Ge_0.84In_0.01Pb_0.1Sb_0.05Te_0.997I_0.003	PC	P	2.10	800	PD + P + B	66
CuS_0.52Te_0.48	PC	P	2.10	1000	PD + P + N + B	67
AgSbTe_1.85Se_0.15	PC	P	2.10	573	PD + P + B	68
(PbTe)_0.86(PbSe)_0.07(Pbs)_0.07 + 2% Na	PC	P	2.10	825	PD + P + N + B	69
Ge_0.89Cu_0.06Sb_0.08Te	PC	P	2.03	750	PD + P + B	70
(Ge_0.87Pb_0.13Te)_0.97(Big₂Te₃)_0.03	PC	P	2.03	773	PD + P + B	71
GeSi nanowires	PC	P	>2.00	RT	U + P + DR	72
Sn_0.99Pb_0.01Se + Se QDs	PC	P	2.00	873	PD + P + N + B	73
Sn_0.985Na_0.015Se	PC	P	2.00	773	PD + P + B	74
Sn_0.97Na_0.03Se	PC	P	2.00	800	PD + B	75
Sb_0.1Ge_0.9Te_0.88Se_0.12	PC	P	2.00	700	PD + P + B	76
PbBi_0.002Te + 15% Ag₂Te	PC	P	2.00	773	PD + P + N + B	77
Pb_0.98Na_0.02Te	PC	P	2.00	773	PD + P + N + U	78
Ge_0.99Bi_0.05Te	PC	P	2.00	650	PD + P + N + B	79
Ge_0.92Cr_0.03 Bi_0.05Te	PC	P	2.00	623	PD + P + N + B	80
Cu₂Se_0.92S_0.09	PC	P	2.00	1000	PD + P + U + B	81
Cu₂Se_0.92S_0.08	PC	P	2.00	1000	PD + P + B	82
Cu₂Se + 0.05 wt% SiC	PC	P	2.00	850	UP + P + N + U	83

2.1 Dimensional reduction and quantum confinement effects

Low-dimensional materials refer to those whose dimensions are close to or smaller than the electron mean free path in at least one or more dimensions. Typical examples include two-dimensional quantum wells, one-dimensional quantum wires or nanotubes, and zero-dimensional quantum dots. Their superior thermoelectric performance primarily stems from the quantum confinement effect in low-dimensional materials.⁸⁴

The quantum confinement effect occurs when the dimensions of a material are reduced to a scale comparable to the de Broglie wavelength of electrons, restricting their motion and quantizing their energy states, as shown in Fig. 6(a). The quantum confinement effect first leads to changes in the material's band structure, as the energy states of electrons split into discrete levels due to spatial confinement, causing the bandgap to narrow and manifesting as changes in the density of states, as shown in Fig. 6(b). Concurrently, the electronic and optical properties exhibit significant differences from their bulk counterparts, mainly manifested in the widening of the bandgap and the blue shift of light emission.⁸⁷ These phenomena originate from electrons and holes being confined within dimensions close to their critical quantum measurements, such as the exciton Bohr radius.


	Fig. 6 (a) Schematic diagram of quantum confinement effect.⁸⁵ Reproduced from ref. 85 with permission from American Chemical Society, copyright (2020). (b) Variation of DOS with dimension reduction of materials.⁸⁶ Reproduced from ref. 86 with permission from Springer Nature, copyright (2017).

In practical applications, quantum dots are confined in three dimensions, quantum wires in two dimensions, and quantum wells in one dimension, representing zero-, one-, and two-dimensional potential wells, respectively. Therefore, due to the quantization of energy bands and the discreteness of energy levels, the distribution of electrons within the energy bands becomes more concentrated. This increases the energy difference generated by carriers under a temperature gradient, thereby enhancing the Seebeck coefficient. There is a direct relationship between the carrier band structure and the Seebeck coefficient, as indicated by eqn (17).⁸⁴


	(17)

In this context, k_B represents the Boltzmann constant, and E_F denotes the Fermi level. Meanwhile, the quantum confinement effect reduces the effective transport path of phonons, thereby increasing phonon scattering and consequently lowering the lattice thermal conductivity, effectively enhancing the thermoelectric figure of merit.⁸⁸ For instance, experimental studies on thin-layer InSe samples have found that the quantum confinement effect sharpens the front edge of the conduction band state density, thereby enhancing the Seebeck coefficient and power factor. This finding underscores the importance of the competition between the quantum confinement length and the thermal de Broglie wavelength in enhancing the power factor.⁸⁹

It is also worth noting that the quantum confinement effect is observed not only in traditionally defined low-dimensional semiconductor materials but also in van der Waals materials. This unusual quantum confinement effect is significant for optoelectronic applications, band engineering, and the design of two-dimensional heterostructures with desirable properties.⁹⁰

Next, we will specifically discuss and illustrate how low-dimensionality and the quantum confinement effect enhance the thermoelectric performance of materials, focusing on two-dimensional, one-dimensional, and zero-dimensional materials.

2.1.1 Two-dimensional materials. In the realm of two-dimensional materials, organic or flexible two-dimensional materials exhibit tremendous potential for wearable devices due to their excellent mechanical and thermoelectric properties.^91,92 The layered structure of two-dimensional materials, characterized by strong in-plane bonding and weak interlayer bonding, helps reduce lattice thermal conductivity while providing anisotropic electronic and phonon transport behaviors.⁹³ These characteristics play a crucial role in decoupling electrical conductivity, Seebeck coefficient, and thermal conductivity.

The low-dimensional features of two-dimensional materials, such as the quantum confinement effect of carriers in two-dimensional superlattices, can enhance the Seebeck coefficient. Additionally, by enhancing interlayer electron transport, it is possible to maintain high electrical conductivity while reducing thermal conductivity, thereby significantly improving thermoelectric performance. Other two-dimensional thermoelectric materials, such as graphene,^94–96 transition metal dichalcogenides,^97–99 and black phosphorus,^100,101 have also garnered widespread attention due to their unique physical and chemical properties. Two-dimensional thermoelectric materials can be fabricated using techniques such as magnetron sputtering,^102–104 flash evaporation,¹⁰⁵ pulsed laser deposition,¹⁰⁶ screen printing,¹⁰⁷ and molecular beam epitaxy.¹⁰⁸

For example, as shown in Fig. 7(a) and (b), a flexible thermoelectric material composed of highly ordered Bi₂Te₃ nanocrystals anchored on a single-walled carbon nanotube (SWCNT) network,⁹¹ exhibits a power factor of approximately 1600 μW m⁻¹ K⁻² at room temperature, which decreases to 1100 μW m⁻¹ K⁻² at 473 K. The maximum thermoelectric figure of merit (ZT) at room temperature reaches 0.89. As shown in Fig. 7(c), Bi₂Te₃ films, with high thermoelectric performance (room temperature ZT of about 1.2) and high flexibility (withstanding 2000 bending tests at a bending radius of 8 mm), demonstrate potential applications in harvesting thermal energy from the environment or the human body.⁹² Additionally, by precisely tuning the deposition of Bi₂Te_2.7Se_0.3 films with an external electric field to deposit anisotropically, unique anisotropic thermoelectric properties can be achieved, resulting in a high room temperature ZT value of about 1.6.¹⁰²


	Fig. 7 (a and b) Illustration of the fabrication and structure of a free-standing highly ordered Bi, Te-SWCNT hvbrid thermoelectric materia.⁹¹ Reproduced from ref. 91 with permission from Springer Nature, copyright (2023). (c) Illustrations of the polycrystalline Bi₂Te₃ film and its state before and after bending.⁹² Reproduced from ref. 92 with permission from Springer Nature, copyright (2019).

Meanwhile, composite thin-film superlattices, as representative two-dimensional thermoelectric materials, are formed by periodically alternating the growth of two different semiconductor thin films. This structural characteristic effectively increases the density of states near the Fermi level and significantly enhances phonon scattering without affecting surface electron scattering, thereby achieving excellent electrical properties and low thermal conductivity. For instance, the first reported nanostructured p-type Bi₂Te₃/Sb₂Te₃ and n-type Bi₂Te₃/Bi₂Te_2.83Se_0.17 superlattice thermoelectric thin films in 2001 achieved an ultra-high thermoelectric figure of merit of 2.4 at room temperature.¹⁰⁹

2.1.2 One-dimensional materials. One-dimensional thermoelectric materials, typically existing in the form of nanowires, nanoribbons, and nanotubes, possess electronic and thermal transport properties distinct from their bulk counterparts. In 1993, Hicks and Dresselhaus proposed the impact of superlattice quantum well structures on the thermoelectric performance of materials.^110,111 The key advantages of one-dimensional thermoelectric materials include quantum confinement, band engineering, and their inherently high surface area to volume ratio, which collectively contribute to their exceptional thermoelectric properties.

One-dimensional structures like nanowires experience stringent spatial confinement, leading to quantum confinement effects. This quantum confinement alters the electronic band structure, thereby enhancing the Seebeck coefficient and subsequently improving thermoelectric conversion efficiency. Quantum confinement can modify the energy at the band edges, facilitating a transition from semimetal to semiconductor. This is beneficial because semiconductors exhibit higher Seebeck coefficients due to their unique valence and conduction bands.¹¹² Additionally, theoretical models demonstrate that quantum confinement in MOSFET channels can cause the Seebeck coefficient to saturate at a non-zero value as the chemical potential increases, distinguishing quantum systems from classical systems and allowing the power factor to increase to a saturation point.¹¹³

The high surface area to volume ratio of one-dimensional thermoelectric materials significantly reduces thermal conductivity, primarily through enhanced phonon scattering mechanisms. This reduction is crucial for improving the thermoelectric figure of merit (ZT) as it allows for maintaining electrical conductivity while minimizing thermal conductivity. Techniques such as element doping or substitution have been successful in further improving thermoelectric performance by effectively reducing lattice thermal conductivity and modifying carrier concentration.¹¹⁴

In practical scientific research, one-dimensional thermoelectric materials are extensively studied. For instance, InAs nanowires synthesized through chemical vapor deposition have achieved thermoelectric performance regulation due to quantum confinement effects.¹¹⁵ Surface-protected, high-mobility modulation-doped GaAs/AlGaAs core–shell NWs exhibit Seebeck coefficients of approximately 65–85 μV K⁻¹, with thermal conductivity as low as about 3 W m⁻¹ K⁻¹, an order of magnitude lower than that of well-prepared but unprotected GaAs NWs, as shown in Fig. 8.¹¹⁶ Other typical representatives include Bi₂Te₃ nanowires,¹¹⁶ PbTe nanowires,¹¹⁷ and carbon nanotubes (CNTs),¹¹⁸ all demonstrating excellent thermoelectric conversion capabilities.


	Fig. 8 (a) SEM image and cross-section schematic of GaAs–AlGaAs core–shell NWs on Si (111) substrate. (b) Power factor for 30 nm NW core (brown) and 5 nm interface region (green).¹¹⁶ Reproduced from ref. 116 with permission from John Wiley and Sons, copyright (2020).

For example, Bi₂Te₃ nanowires have been widely studied for their outstanding thermoelectric performance. In their one-dimensional form, Bi₂Te₃ exhibits high Seebeck coefficients and low thermal conductivity, thereby improving their ZT values. PbTe nanowires also show remarkable thermoelectric performance, with their one-dimensional structure enhancing electron transport properties and reducing thermal conductivity. Carbon nanotubes are considered potential candidates for high-performance thermoelectric materials due to their unique electron transport characteristics and extremely low thermal conductivity.

Yang et al.¹¹⁹ reported the synthesis of large-area, wafer-scale silicon nanowire hole arrays, achieving a ZT value of 0.71 at 700 K, approximately 18 times higher than bulk silicon, as shown in Fig. 9(a)–(g). Warittha et al.¹²⁰ demonstrated a promising hybrid nanowire, which was integrated into a self-assembled hybrid thermoelectric nanofilm's three-dimensional network for scalable thermoelectric applications. Scaling up this nanostructured material led to the construction of a thermoelectric generator with universal pipeline insulator geometry. This device exhibited a power factor of 7.45 μW m⁻¹ K⁻², a ZT value of 0.048, an output power of 130 μW, and operational stability for 15 days at ΔT = 60 K, as shown in Fig. 9(h)–(i).


	Fig. 9 SiNW fabrication, morphology, and thermoelectric measurement with a suspended microdevice. Schematic of fabrication: (a) nanoimprint lithography to pattern metals, (b) MACE to create porous SiNW array, (c) post-doping with SOD and annealing, (d) SEM image of porous SiNW. TEM images of SiNWs with porosities (e) 9% and (f) 61%. (g) False-color SEM of suspended microdevice with a porous SiNW bridging membranes for thermoelectric measurement. Pt leads for heating and sensing marked red and blue. Electrical resistance measured by four-probe method.¹¹⁹ Reproduced from ref. 119 with permission from American Chemical Society, copyright (2021). (h) Schematic of hybrid TE material/device process: (1) synthesis of Bi₂Te₃-PEDOT:PSS hybrid nanowire, (2) fabrication of nanowire-embedded PEDOT:PSS nanofilms, (3) Construction of TE device for energy harvesting. (i) TEM of single Bi₂Te₃ nanowire, high magnification, with SADP insets.¹²⁰ Reproduced from ref. 120 with permission from Springer Nature, copyright (2019).

2.1.3 Zero-dimensional materials. Zero-dimensional thermoelectric materials, also known as quantum dots, are solids with nanoscale dimensions in all three spatial directions. These materials are smaller than the electron mean free path, causing both electrons and phonons to exhibit unique quantized energy levels and sharp density of states due to quantum confinement.¹²¹ This leads to significant potential applications in thermoelectric conversion. Due to the strict confinement of electrons and phonons in quantum dots, their energy level distribution changes, which can improve the band structure, enhance the Seebeck coefficient, and increase thermoelectric efficiency.^122,123 Fine-tuning the size of quantum dots can optimize thermoelectric performance, while their low thermal conductivity is due to significantly enhanced phonon scattering. Zero-dimensional thermoelectric materials can also be combined with other materials, such as polymers or composites, to create multifunctional thermoelectric solutions.

For example, PbSe/Te/PbTe quantum dot superlattices¹²⁴ have shown significant improvements in Seebeck coefficient and thermoelectric figure of merit (ZT) compared to bulk materials, with ZT values as high as 0.9 and potentially higher at elevated temperatures. Research by T. Harman et al.¹²⁵ on PbSeTe-based quantum dot superlattice structures further illustrates these benefits. Additionally, superlattice-structured nanowires¹²⁶ have demonstrated excellent performance in low-temperature thermoelectric cooling, maintaining high coefficient of performance (COP) even under high cooling rates.

Nugraha et al.¹²⁷ prepared colloidal quantum dot (CQD) thermoelectric materials, which show promise for emerging thermoelectric generator (TEG) technology operating near room temperature due to their solution processability, scalable manufacturing potential, and ability to tune the Seebeck coefficient and thermal conductivity, as illustrated in Fig. 10. Nugraha et al.¹²⁸ further utilized chemical doping to enhance electron transport while maintaining low thermal transport, leading to enhanced n-type thermoelectric behavior in colloidal quantum dot films embedded in a metal halide matrix, with low thermal conductivity, as shown in Fig. 11. Shi et al.¹²⁹ fabricated polymer-quantum dot composite films that included well-protected Te quantum dots, exhibiting a high power factor and representing a potential example of quantum dot thermoelectric materials.


	Fig. 10 (a) Schematic of OA ligand exchange using diferent iodide salts, (b) ETIR, and (c) optica absorption spectra ofCoD films treated with different iodide salts.¹²⁷ Reproduced from ref. 127 with permission from John Wiley and Sons, copyright (2019).


	Fig. 11 (a) Schematic depicting a Pbs COD covered by the Pbl, matrix. Temperature-dependent(b) Seebeck coefficient and power factor, and (c) electrical conductivity in Pbs COD films with Pbl, matrix (d) schematic of an n-doped Pbs COD with Pbl, matrix using Cs₂CO, as the n-type dopant. (e) Temperature-dependent electrical conductivity.¹²⁸ Reproduced from ref. 128 with permission from American Chemical Society, copyright (2021).

2.2 Point defect engineering

Point defects refer to atomic-scale imperfections in the crystal lattice of a material, including vacancies, interstitial atoms, and dopant atoms. From a thermodynamic perspective, vacancies are a type of thermodynamic equilibrium defect due to the balance between vacancy formation energy and entropy increase. Point defects play a crucial role in tuning the performance of thermoelectric materials, as illustrated in Fig. 12. The formation potential of target point defects can generally be assessed using first-principles density functional theory (DFT) calculations to determine the likely formation of vacancies.¹³²


	Fig. 12 Synergistic control of the carrier and phonon transports via defect engineering.¹³⁰ (a) Schematic of carrier and phonon transport control in GeTe-based compounds with hierarchical structures.¹³⁰ (b) Weighted mobility (μ_w) and μ_w/κ_L ratio of Ge-deficient samples sintered at 873 K vs. 723 K.¹³⁰ Reproduced from ref. 130 with permission from Springer Nature, copyright (2022). (c) ZT value vs. reduced Fermi potential with different quality factors at 648 K.¹³¹ (d) Schematic of Te atom escape during annealing, showing vacancy engineering effects.¹³¹ (e) Band structure of Te with varying vacancy ratios: no vacancy, 1/81, 1/54, 1/36; Fermi level shifts into the valence band with increasing vacancies.¹³¹ Reproduced from ref. 131 with permission from Elsevier, copyright (2021).

Point defects can be introduced and controlled through various methods: doping:^133–135 the predominant technique involves integrating foreign atoms, or dopants, into the crystal lattice of the material. Doping can be effected via methods such as melting, mechanical alloying, chemical synthesis, chemical vapor deposition (CVD), and physical vapor deposition (PVD). Thermal treatment:^30,33,131 high-temperature treatments can regulate vacancies and interstitial atoms within the material. These processes typically involve annealing and rapid thermal processing. These high-temperature processes include annealing and rapid thermal processing. Ion implantation:^136,137 high-energy ion bombardment on the material's surface facilitates the introduction of point defects. This technique affords precise control over both the depth and concentration of the introduced dopants. Mechanical stress:¹³⁸ external forces, such as stretching or compressing, are employed to influence the distribution of interstitial atoms or vacancies within thermoelectric materials.

Impact of point defects on thermoelectric materials, affecting electrical conductivity: doping atoms can provide additional free charge carriers (electrons or holes), thereby increasing the electrical conductivity of the material. The type (donor or acceptor) and concentration of the dopant atoms have a significant impact on the material's electrical conductivity. Modifying Seebeck coefficient:^139,140 point defects can indirectly influence the Seebeck coefficient by altering the band structure of the material, thereby affecting the transport properties of charge carriers. Reducing thermal conductivity: point defects can enhance phonon scattering within the lattice, thereby reducing thermal conductivity. This is crucial for improving the thermoelectric figure of merit (ZT value). For example, Li et al.¹⁴¹ used Bi/Cu double vacancies to synergistically optimize the electrical and thermal properties of BiCuSeO, as shown in Fig. 13. Bi/Cu vacancies and grain boundaries favor short- and long-wavelength phonon scattering. Adjacent superlattice interfaces can strongly scatter mid-wavelength phonons, achieving full-spectrum phonon scattering. These vacancies effectively scatter phonons without deteriorating electrical transport, thus exhibiting excellent thermoelectric performance. Influencing mechanical properties: point defects can potentially enhance the mechanical strength of materials.^142–144 Affecting carrier concentration and mobility: point defects (especially dopant atoms) can change the carrier concentration,^145–147 which is crucial for tuning the thermoelectric performance of materials. The presence of point defects also influences the mobility of charge carriers.¹⁴⁸


	Fig. 13 Positron annihilation spectrometry characterization of the Bi_1−xCu_1−ySeO samples, showing the interlayer charge transfer in Bi/Cu dual-vacancies Bi_0.975Cu_0.975SeO sample. (a) Positron lifetime spectrum of Bi_1−xCu_1−ySeO samples. (b) Schematic representation of trapped positrons for Bi_1−xCu_1−ySeO samples in (100) plane. (c) Schematic representation of various phonon scattering mechanism in BiCuSeO with Bi/Cu vacancies.¹⁴¹ Reproduced from ref. 141 with permission from American Chemical Society, copyright (2015).

2.3 Nanocomposites

Nanocomposites refer to composite materials composed of at least two different components, with at least one component having nanoscale dimensions. These materials typically consist of nanoparticles, nanowires, nanosheets, or other nanostructures combined with a matrix material. This combination not only improves the thermoelectric properties of the original materials but also imparts new physical and chemical characteristics. Methods to achieve nanocomposites include: mechanical synthesis: physically mixing and milling nanoparticles or other nanostructures with the matrix material, a simple and effective method suitable for large-scale production.^149,150 Solution synthesis:^151–153 using chemical solution deposition to mix different components at the molecular level, achieving more uniform nanoparticle dispersion. Chemical vapor deposition (CVD) and physical vapor deposition (PVD):^154–157 depositing nanoparticles on the surface of the matrix material to form nanocomposites. Self-assembly:^158,159 this approach utilizes molecular interactions to autonomously organize nanostructures into ordered composite materials, facilitating the construction of highly organized architectures at the nanoscale. Co-deposition:^160,161 this technique involves the simultaneous deposition of matrix materials and nano-fillers, enabling the integrated formation of composites through a synergistic process.

The impact of nanocomposites on the performance of thermoelectric materials:

2.3.1 Reducing thermal conductivity. Nanocomposites enhance the internal phonon scattering mechanisms by introducing nanoscale interfaces. Phonons, the carriers of thermal energy, experience scattering across these interfaces, which reduces their propagation efficiency within the material. Additionally, nanoscale structures can induce phonon localization effects, further reducing thermal conductivity. Increasing the Seebeck coefficient: nanocomposites can boost the Seebeck coefficient through band engineering and quantum confinement effects. At the nanoscale, the electronic band structure is altered due to quantum confinement, enhancing the material's thermoelectric sensitivity. Furthermore, band alignment and electron filtering effects can also be exploited in nanocomposites to improve the Seebeck coefficient, as illustrated in Fig. 14.^162,163


	Fig. 14 (a and b)Schematic diagram of the energy filtering effect.^162,163 Reproduced from ref. 162 with permission from John Wiley and Sons, copyright (2020). Reproduced from ref. 163 with permission from Elsevier, copyright (2022).

2.3.2 Adjusting electrical conductivity. Nanocomposites are engineered to optimize electrical conductivity by either enhancing or modulating electron transport pathways. Incorporation of nanoparticles introduces additional electron transport channels within the matrix material or augments electron mobility through the formation of band structures. Improving mechanical stability: nanocomposites exhibit superior mechanical stability compared to single-component materials, a feature of critical importance for thermoelectric materials that frequently operate under the duress of thermal gradients and mechanical stresses. The structural composition of nanocomposites enhances crack resistance and elasticity, thus bolstering the reliability and longevity of thermoelectric devices. Enhancing multifunctionality: nanocomposites facilitate the integration of diverse functionalities. For example, nanoparticles can be utilized to endow thermoelectric materials with specific properties such as magnetism, catalysis, or optical activity. Flexibility in manufacturing: the array of available preparation techniques for nanocomposites allows for considerable flexibility in the design and fabrication of tailored thermoelectric materials. A variety of synthesis methods and processing techniques are available to precisely engineer the microstructure and macroscopic properties of nanocomposites.

2.3.3 Optimizing carrier concentration. Nanocomposite technology enables precise control over the carrier concentration within materials, a critical factor for the overall performance of thermoelectric materials. Optimization of carrier concentration can be achieved by selecting suitable dopants, adjusting the distribution of nanoparticles, or changing the chemical composition of the matrix material. As shown in Fig. 15, two different nanostructures were produced from an amorphous precursor based on crystalline NbCo_1.1Sn composition—one containing only half-Heusler grains, and the other containing both half-Heusler grains and full-Heusler nanoscale precipitates. The enhancement in the Seebeck coefficient of samples containing nanoscale precipitates is attributed to the filtering effect of low-energy and low-mobility electrons at the half-Heusler and full-Heusler interfaces, along with the formation of cobalt interstitial defects in the half-Heusler matrix.


	Fig. 15 (a) HR-TEM image, (b) EDX elemental maps of as-spun amorphous NbCo_1.1Sn. (c) Chemical compositions of as-spun amorphous NbCo_1.1Sn acquired from various methods. (d) APT reconstruction of as-spun amorphous NbCo_1.1Sn and (e) 1st, 3rd and 5th nearest neighbor distribution for each alloying element. (f) TEM image of an APT tip with aperture (SAED pattern included as an inset). (g) STEM-HAADF image, and (h) 3d atom maps of NCS-893, including iso-concentration surfaces of 38 at% Co (insets show enlarged views of the regions marked by dashed rectangular boxes), and the proxigrams based on iso-concentration surfaces of 38 at% Co for (i) spherical nano-precipitates, (j) disk-shaped nano-precipitates, and (k) full-Heusler grain.¹⁶⁴ Reproduced from ref. 164 with permission from Elsevier, copyright (2021).

Solution synthesis of SnSe demonstrates excellent control over the growth of nanoscale grains, and due to strong phonon scattering at the nanoscale grain boundaries, nanocrystalline SnSe exhibits an ultralow thermal conductivity.¹⁶⁵ In BiSbTe, the combination of defect complexity and nanostructuring has been proven effective, as evidenced by the achieved ZT value of 1.4 at 400 K in zinc-doped BiSbTe alloys (specifically Bi_0.46Sb_1.54Te₃).¹⁶⁶ A significant enhancement in ZT is observed in Gd–Cu₂Te upon co-doping with n-type PbSe. Additionally, a unique semi-coherent interface between the PbSe matrix and Cu₂Se nanoscale precipitates has been noted. This type of nanoscale precipitate, along with its semi-coherent interface, achieves an ultralow lattice thermal conductivity by scattering thermal-carrying phonons, as shown in Fig. 16.¹⁶⁷


	Fig. 16 (a and b)Schematic illustration of the semi-coherent interface between the PbSe matrix and Cu₂Se nanoprecipitates, showing phonon scattering of heat-carrying phonons.¹⁶⁷ Reproduced from ref. 167 with permission from John Wiley and Sons, copyright (2024).

Zhao et al.¹⁶⁸ have achieved dual control over phonon and electron transport properties by embedding soft magnetic material nanoparticles into a thermoelectric matrix, as shown in Fig. 17. The superparamagnetic behavior of the nanoparticles leads to three thermomagnetic effects: charge transfer from the magnetic inclusions to the matrix; multiple electron scattering induced by superparamagnetic fluctuations; and enhanced phonon scattering caused by magnetic fluctuations and the nanostructures themselves. These effects synergistically manipulate electron and phonon transport on the nano and mesoscale, effectively enhancing the thermoelectric performance of the fabricated nanocomposite materials.


	Fig. 17 Microstructures of xCo/Ba_0.3In_0.3Co₄Sb₁₂ (x = 0.2%): (a) SEM images of powders. (b) SEM images of bulk material. (c and d) HRTEM images. Co nanoparticles (5–10 nm diameter) induced thermoelectromagnetic effects: (e) UPS spectrum of Ba_0.3In_0.3Co₄Sb₁₂ matrix; inset shows spectrum's ringed areas, focusing on cut-off E_cut-off (I) and Fermi edge E_F (II). Units are arbitrary. (f) Charge transfer schematic from Co nanoparticles' 4s electrons to the matrix; including energy levels and work functions of both. (g) XPS of Sb 3d_5/2 and 3d_3/2 core levels in xCo/Ba_0.3In_0.3Co₄Sb₁₂ with varying x values; highlights peak positions in the matrix and for different Co concentrations. (h) Interface band bending away from interface due to charge transfer from Co nanoparticles to matrix. (i) Electron scattering at xCo/Ba_0.3In_0.3Co₄Sb₁₂ interfaces caused by interface potential VB, affecting electron energy. (j) Single electron scattering due to s–d spin coupling in ferromagnetic Co nanoparticles; magnetic moment is fixed. (k) Multiple electron scattering within superparamagnetic Co nanoparticles due to random magnetic domain movements.¹⁶⁸ Reproduced from ref. 16 with permission from Springer Nature, copyright (2017).

2.4 Band engineering

As derived from the theories of electrical and thermal transport in the introduction section of Chapter 1 (eqn (5)–(12)), there is a close relationship between the electrical properties of materials and their band structures. Therefore, by adjusting the band structure, the energy conversion efficiency of thermoelectric materials can be effectively enhanced. Predicting and simulating the evolution of band structures can also effectively forecast the thermoelectric performance of materials, as illustrated in Fig. 18.¹⁶⁹ Common methods for adjusting band structures primarily include the following: (1) effective mass of carriers;^170–173 (2) resonance states;^174–177 (3) controlling the degeneracy of energy bands;^178–181 (4) band convergence and bandgap tuning.^52,182–184 These methods are key strategies for controlling the electrical properties of thermoelectric materials and are of significant importance for improving thermoelectric conversion efficiency.


	Fig. 18 The evolution of band structure models used in this study. (a) A single-band changes in effective mass. (b) One band (orange) changes in effective mass while another band (blue) is fixed. (c) The valence band (orange) changes in effective mass while the conduction band (blue) is fixed.¹⁶⁹ Reproduced from ref. 169 with permission from Springer Nature, copyright (2021).

2.4.1 Carrier effective mass. Generally speaking, with a fixed carrier concentration, a larger effective mass indicates an increased density of states in the energy band, which enhances the Seebeck coefficient. However, an increase in carrier effective mass also affects the material's electrical conductivity. A larger effective mass typically reduces the mobility of carriers. Therefore, although a larger effective mass is beneficial for increasing the Seebeck coefficient, it can simultaneously lead to a reduction in electrical conductivity, which is detrimental to the overall performance of thermoelectric materials. Thus, finding the optimal balance between carrier effective mass and other thermoelectric parameters is crucial when designing and optimizing thermoelectric materials. Ideally, this involves maintaining a high Seebeck coefficient while minimizing the negative impact on electrical conductivity. In practical applications, the effective mass of carriers can be modulated through doping or by utilizing quantum confinement effects.

For example, although an increase in effective mass typically leads to a dramatic deterioration in carrier mobility, thus limiting further improvements in thermoelectric performance. Su et al.¹⁸⁵ demonstrated that anisotropic scattering factors can enhance both the carrier mobility and the Seebeck coefficient in n-type tin selenide (SnSe) crystals doped with iodine, perpendicular to the plane. By altering the scattering factor (r), they significantly increased the average dimensionless figure of merit (ZT_ave) from 0.84 to 1.57 over the temperature range of 300–773 K, offering a novel strategy for optimizing thermoelectric performance. He et al.¹⁸⁶ reported on the temperature-dependent interaction of three distinct electronic bands in tin sulfide (SnS) crystals, as shown in Fig. 19. This behavior led to a synergistic optimization of effective mass (m*) and carrier mobility (μ), reducing the effective mass and increasing mobility, thereby raising the power factor from 30 to 53 μW cm⁻¹ K⁻². Additionally, Se alloying decreased the thermal conductivity, achieving a maximum figure of merit (ZT_max) of about 1.6 at 873 K and an average ZT (ZT_ave) of about 1.25 across the range from 300 to 873 K. This provides diverse pathways for optimizing thermoelectric performance through band structure manipulation.


	Fig. 19 (a) Schematic: modifying carrier effective mass through band sharpening. (b) Evolution of three valence bands with increasing temperature in SnS. Top: VBM2 (blue) moves away from VBM1 (red), VBM3 (green) approaches VBM1, and VBM2 crosses VBM3. Bottom: Energy gap (ΔE) between VBM1 and VBM2, and VBM1 and VBM3 in SnS_1−xSe_x as temperature changes. (c) Effective masses for VBM1, VBM2, and VBM3 in SnS_1−xSe_x decrease with Se alloying. (d) Pisarenko plots: Seebeck coefficients vs. carrier concentration for different band models. (e) Carrier mobility vs. carrier concentration for different band models. (f) Seebeck coefficient × carrier mobility vs. carrier concentration in SnS_1−xSe_x crystals, showing the interplay of three bands. (g) Simulated power factor vs. carrier concentration for different band models. Inset: Quality factor ratio (β/β₀) in SnS_1−xSe_x vs. SnS. Experimental data match TKB model, indicating three-band contribution. SKB: single Kane band; DKB: double Kane band; TKB: triple Kane band.¹⁸⁶ Reproduced from ref. 186 with permission from The American Association for the Advancement of Science, copyright (2019).

2.4.2 Resonant states. Resonant states refer to localized energy levels in the band structure of solid materials, which arise due to certain atoms or defects. These levels are close to the edge of the conduction or valence bands, forming what is termed a “resonant” state. The concept of resonant states was initially proposed in the 20th century in the study of metals, then termed “virtual bound states.” They provided a novel way to alter the state density in solids.¹⁸⁷ When impurity atoms are introduced into a periodic crystal lattice, the original lattice periodicity is disrupted. This results in a change in the charge distribution around the impurity, thereby disturbing the original periodic potential field. A significant alteration occurs in the state density near the impurity energy level (provided that the Fermi level is in an appropriate position), resulting in the formation of resonant states. Another classic expression for the Seebeck coefficient, the Mott formula, plays a vital role in qualitatively analyzing changes in the Seebeck coefficient:


	(18)

where k_B is the Boltzmann constant, e is the electron charge, E is the electron energy, τ is the carrier relaxation time, and E_F is the Fermi energy.

As shown in Fig. 20(a) and (b), the characteristic of resonant states is the pronounced peak within a narrow energy range E_R, where the density of states is significantly elevated. According to the Mott formula, the emergence of resonant states is very beneficial for enhancing thermoelectric performance because it increases the rate of change in the density of states at the Fermi level, thereby improving the Seebeck coefficient while essentially maintaining the electrical conductivity unchanged.¹⁸⁹


	Fig. 20 Displays the calculated density of states (DOS) for different materials, including: (a) rhombohedral phase GeTe (Ge₆₄Te₆₄) and In_0.016Ge_0.984Te (InGe₆₃Te₆₄) at room temperature; (b) cubic phase Ge₆₄Te₆₄ and InGe₆₃Te₆₄ at high temperatures. In both phases of InGe₆₃Te₆₄ at the Fermi level (E_F), there is a pronounced change in the DOS, indicating resonant energy levels.¹⁸⁸ Reproduced from ref. 188 with permission from Springer Nature, copyright (2017).

The Seebeck coefficient is related to the energy filtering effect of the material's carriers. When resonant states are close to the Fermi level, they can alter the energy distribution of carriers, thereby enhancing the energy filtering effect and increasing the density of states near the Fermi level, which in turn boosts the Seebeck coefficient. Thus, by precisely controlling the energy position of resonant states, the Seebeck coefficient of thermoelectric materials can be effectively enhanced. Additionally, resonant states can also impact the material's electrical conductivity. Since resonant states increase the density of states near the conduction or valence bands, under specific conditions, they can enhance the concentration and mobility of carriers, thereby improving the electrical conductivity, an effect particularly pronounced in semiconductor materials.

Optimization strategies involving resonant states have been extensively studied. For instance, Pan¹⁹⁰ examined the resonant effects of Tl in PbSe and developed a Boltzmann transport model to understand the variations in Seebeck coefficient and mobility induced by resonant energy levels at different temperatures. They discovered that the most critical characteristic of resonant levels for thermoelectric materials is their central energy position, optimally situated slightly into the conduction band from the band edge. Meanwhile, the model also confirmed that moderate performance improvements using resonant levels are feasible in systems similar to PbSe. Shen et al.¹⁹¹ employed band unfolding techniques and density functional theory to study the doping effects of group III elements (Al, Ga, In, and Tl) and group V elements (As and Sb) on BiCuSeO. Their research revealed significant resonant states introduced near the conduction band minimum and valence band maximum by In and Tl, respectively, providing guidance for enhancing thermoelectric efficiency through band engineering. They also calculated decomposed density of states and charge density to elucidate the origins of the resonant effects. The Bhat team¹⁹² reported using first-principles density functional theory calculations to introduce Zn as a resonant dopant in SnTe. They demonstrated that Zn-induced resonant states elevate the heavy hole valence band above the light hole valence band, thus elevating the Seebeck coefficient (approximately 127 μV K⁻¹ at 300 K) and figure of merit ZT (about 0.28 at 300 K) of the SnTe base material to higher levels. Transport properties calculated using the Boltzmann transport equation predicted that Zn-doped SnTe is a promising thermoelectric (TE) material, further confirmed by experimental findings with a maximum ZT value of about 1.49 at 840 K and an average ZT value of about 0.78 with cold and hot ends at 300 K and 840 K, respectively. Zhang et al.¹⁹³ achieved ultralow lattice thermal conductivity and high thermoelectric performance in GeTe thermoelectric materials doped with indium and heavily co-doped with copper. Indium doping, by introducing resonant energy levels, increased the density of states near the Fermi surface of GeTe, significantly enhancing the Seebeck coefficient, as shown in Fig. 21.


	Fig. 21 (a) Super-low lattice thermal conductivity and high thermoelectric performance are achieved in GeTe thermoelectric materials through doping with In and a substantial amount of Cu. Indium doping enhances the state density near the Fermi surface of GeTe by introducing resonant energy levels, resulting in a significant increase in the Seebeck coefficient. (b and c) Electronic density of states of GeTe ((b) R–GeTe and (c) C–GeTe, the black lines) and the corresponding In doping (RGe_0.984TeIn_0.0156 and C–Ge_0.984TeIn_0.0156, the red lines).¹⁹³ Reproduced from ref. 193 with permission from American Chemical Society, copyright (2021).

2.4.3 Band degeneracy. Band degeneracy refers to the number of electronic states at the same energy level within a material's band structure. Due to the interactions between quantum mechanical wave functions and the crystal potential field, the energy states of electrons are quantized and form discrete energy bands. In some cases, due to crystal symmetry or other quantum effects, different electronic orbital states may possess the same energy, resulting in band degeneracy. Degeneracy typically occurs near the extrema (top or bottom) of energy bands. A high degree of degeneracy can increase the channels for electron (or hole) transport without increasing the carrier concentration, thus enhancing electrical conductivity. Moreover, since the Seebeck coefficient is related to the carrier energy distribution, degenerate bands can maintain lower thermal conductivity while enhancing the Seebeck coefficient. Therefore, optimizing band degeneracy is one of the key strategies for improving the ZT value of thermoelectric materials. For instance, Zhang¹⁹⁴ chose to mix VCoSn and TaCoSn (E_X₂ − E_X₃ = −0.36 eV) in studies regulating the conduction band degeneracy in half-Heusler thermoelectric materials. When the mixing ratio reached 0.5, degeneracy occurred at both types of X points, successfully validating the results of the orbital phase diagram. This indicates that analyzing orbital contributions can provide new insights into controlling band degeneracy and optimizing and designing efficient half-Heusler thermoelectric materials, as shown in Fig. 22.


	Fig. 22 (a) The conduction band edges of half-Heusler compounds are primarily composed of the d orbitals of the X and Y elements. The circle size represents n-type conductivity mass at 10²⁰ cm⁻³ under 900 K. Two conduction band minima (CBM) at the X point (N = 3) are dominated by X atoms (E_x₁, red) and Y atoms (E_x₂, green). In ZrNiSn (b), Y forms the CBM, while in NbFeSb (c), X forms the CBM. In NbCoSn (d), these CBMs converge, doubling the valley degeneracy to 6 (N = 6).¹⁹⁴ Reproduced from ref. 194 with permission from Royal Society of Chemistry, copyright (2022).

According to eqn (19), increasing N_V can enhance the effective mass (m*), thereby boosting the corresponding Seebeck coefficient. This has been validated in the literature.¹⁹⁵


	(19)

When multiple bands have the same or similar energy, band degeneracy can be increased in two ways: firstly, through orbital degeneracy of the bands (i.e., multiple bands having the same or close energies); secondly, by exploiting crystal symmetry to cause degeneracy of multiple valleys in the Brillouin zone (i.e., valley degeneracy).¹⁹⁶ For example, in the FeNbSb compound, the conduction band at the X point has a degeneracy of 3, while the valence band at the L point has a higher degeneracy (N_v = 8).¹⁹⁷ Based on these scenarios, research on band convergence can be broadly categorized into two types: the first involves converging different bands through alloying or changing temperature to achieve greater orbital degeneracy. Lead chalcogenides and Mg₂(Si, Sn) solid solutions are typical examples.^198,199 The second type of study involves altering the crystal symmetry to achieve greater valley degeneracy, as seen in tetragonal phase chalcopyrites, CaAl₂Si₂-type Zintl compounds, and (Bi, Sb)₂Se₃ solid solutions^200–203, as shown in Fig. 23.


	Fig. 23 Valence band structure of PbTe_1−xSe_x (a) Valence band structure of PbTe_1−xSe_x. Brillouin zone showing low degeneracy hole pockets (orange) at the L point and high degeneracy hole pockets (blue) along the Σ line. There are 8 half-pockets at L (N_v = 4) and 12 valleys at Σ (N_v = 12). (b) Relative energy of valence bands in PbTe_0.85Se_0.15. At ∼500 K, the valence bands converge, allowing transport contributions from both L and Σ bands. C: conduction band; L: low degeneracy hole band; Σ: high degeneracy hole band.¹⁹⁵ Reproduced from ref. 195 with permission from Springer Nature, copyright (2011).

2.4.4 Band convergence and band gap tuning. Band convergence refers to a phenomenon in certain materials where multiple energy bands approach or intersect, leading to an increased density of electronic states at these energy levels. This results in changes to the effective mass and carrier mobility. Fundamentally, band convergence manifests as higher carrier concentration (n) under a given Fermi level (E_F) when multiple bands align energetically. This can increase the effective mass of electrons (or holes), where a higher effective mass typically implies “flatter” bands. This flattening causes carriers to experience more significant energy changes under thermal perturbations, thereby increasing the Seebeck coefficient. While an increase in effective mass might reduce carrier mobility and thus decrease electrical conductivity, band convergence can offset this by increasing carrier concentration. This happens because more bands participate in the conduction process, allowing for more carriers to be available at the same chemical potential.

At present, band convergence remains a very important thermoelectric optimization strategy. For example, research by Ransell D'Souza et al.²⁰⁴ suggests that band convergence can significantly enhance thermoelectric performance, as evidenced by increases in the thermoelectric power factor and ZT value. However, the impact of intervalley scattering near the band convergence temperature continues to be an area of ongoing research.

Verma et al.²⁰⁵ observed a significant improvement in thermoelectric performance in p-type TiCoSb half-Heusler alloys, achieved by increasing the effective mass of the state density due to the convergence of two valence band maxima. The concept of band convergence is not limited to theoretical studies but has also been practically applied in various materials, as illustrated in Fig. 24. For instance, the co-doping strategy in materials such as SnTe shows that band convergence can improve the Seebeck coefficient, thereby enhancing thermoelectric performance.²⁰⁶ Similarly, doping Pb in GeTe-based alloys results in band convergence, helping to maintain a high power factor while reducing carrier density, thereby maximizing the thermoelectric figure of merit (ZT).²⁰⁷


	Fig. 24 Schematic illustration of the significant enhancement in thermoelectric figure of merit ZT due to band convergence.²⁰⁵ Reproduced from ref. 205 with permission from American Chemical Society, copyright (2022).

Potential challenges and limitations: Wu et al.²⁰⁸ argue that while band convergence offers several advantages, it also brings challenges. For instance, neglecting intervalley scattering may lead to inaccurate estimates of electron–phonon scattering and thermoelectric transport properties, highlighting the necessity of carefully considering these factors in material design. Park et al.²⁰⁹ demonstrated through first-principles treatment of electron–phonon scattering in the CaMg₂Sb₂–CaZn₂Sb₂ Zintl system and the full Heusler alloy Sr₂SbAu that the benefits of band convergence can be essentially offset by interband scattering, depending on how the bands converge. In the Zintl alloys, band convergence did not improve weighted mobility or the effective mass of the state density. The fundamental reason is that the bands converge at a single k-point, triggering strong deformation potential and polar optical interband scattering. This contrasts with band convergence at distant k-points (as in the full Heusler alloys), which better preserves single-band scattering behavior, thereby successfully leading to performance improvement. Therefore, it is suggested that band convergence as a thermoelectric design principle is most suitable for situations occurring at distant k-points.

Band gap and its influence on thermoelectric materials the band gap refers to the energy interval between the conduction band and the valence band as shown in Fig. 25, significantly influencing the performance of thermoelectric materials. When the temperature increases, minority carriers in the band gap are thermally excited. This not only substantially reduces the overall thermoelectric potential but also causes the thermoelectric potential to cease increasing with temperature. Additionally, the contribution of electrons (bipolar) to thermal conductivity increases with temperature.^211,212 These two factors together lead to the figure of merit ZT peaking at a certain temperature. Hence, the band gap of thermoelectric materials fundamentally limits the peak of ZT. Theoretically, a higher ZT at elevated temperatures could be achieved by increasing the band gap while keeping all other physical parameters constant.²¹¹ Based on this principle, a strategy has been proposed: to prevent the degradation of thermoelectric performance at high temperatures due to thermally excited minority carriers by increasing the band gap. This strategy involves introducing wide-bandgap compounds into thermoelectric materials to enhance the band gap and, consequently, improve thermoelectric performance.


	Fig. 25 Schematic illustration of band gap tuning strategy.²¹⁰ Reproduced from ref. 210 with permission from John Wiley and Sons, copyright (2023).

Band gap tuning strategies have been extensively applied. For instance, Chegel et al.²¹³ adjusted the band gap of materials through methods such as bias tuning and chemical doping to optimize electrical conductivity. In tetragonal germanene (T-Ge), this optimization enhanced thermoelectric performance and resulted in a higher figure of merit (ZT). Zhang et al.²¹⁴ improved the power factor by increasing the carrier concentration in thermoelectric materials through altering the Fermi level and narrowing the band gap, which directly promoted better thermoelectric performance. Su et al.²¹⁵ in materials like n-type Bi_1.5Sb_0.5Te₃, expanded the band gap through isoelectronic substitution, increasing the Seebeck coefficient and suppressing bipolar thermal conductivity, thereby reducing the lattice thermal conductivity and leading to higher ZT values at specific temperatures. K. Berland et al.²¹⁶ demonstrated that band gap tuning in low-gap compounds like MgSc₂Hg and Li₂CaSi could lead to promising thermoelectric performance under appropriate doping. Teng-Yu Su et al.²¹⁷ showed that in layered thin films such as PtSe₂, thermally induced band gap opening exhibited exceptional thermoelectric performance, illustrating how band gap adjustments affect the properties of layered materials.

Hasdeo et al.²¹⁸ found that for 2D Dirac materials, opening the band gap within an optimal range (6 kBT to 18 kBT) maximizes the figure of merit (ZT), eliminating the cancellation effect of electron–hole pair transport. Chen et al.²¹⁹ studied how expanding the band gap in certain materials could inhibit bipolar excitation, thus improving the Seebeck coefficient and reducing thermal transport contributions, particularly benefiting thermoelectric performance near room temperature. Airan Li et al.²¹² proposed a strategy to open the band gap by introducing d–d orbital interactions, resulting in significantly improved n-type and p-type thermoelectric performance compared to the metallic MgNiSb, as demonstrated in Fig. 25 and 26.


	Fig. 26 (a) Simplified schematic of bandgap formation in HHs at the Γ-point based on molecular orbital theory. When X is a transition metal, symmetry-permitted d–d orbital interaction opens the bandgap in HH XYZ, whereas for main-group metals, symmetry-forbidden d–s orbital interaction does not. (b) DOS and projected DOS of CoSb, TiCoSb, and MgCoSb. (c) DOS and projected DOS of NiSb, TiNiSb, and MgNiSb.²¹⁰ Reproduced from ref. 210 with permission from John Wiley and Sons, copyright (2023).

2.5 Phonon engineering

From the thermal transport theory presented in the introduction, it is understood that lattice thermal conductivity is solely related to phonon transport processes and is not directly linked to electrical conductivity and the Seebeck coefficient. Therefore, it can be regulated as an independent parameters shown in Fig. 27. In the section on nanocomposite strategies, we have already touched upon examples where phonons are scattered, thereby reducing lattice thermal conductivity. Hence, in this section, we will provide a brief discussion of this strategy from different perspectives.


	Fig. 27 Schematic illustration of dislocations scattering phonons without hindering electron movement.²²⁰ Reproduced from ref. 220 with permission from American Chemical Society, copyright (2019).

Phonon engineering primarily enhances the thermoelectric figure of merit by regulating lattice thermal conductivity. For instance, Xu and colleagues²²¹ reported an average ZT value (ZT_ave) of 0.90 for n-type PbSe-based thermoelectric materials at low temperatures (300–573 K) and 0.96 at low to mid temperatures (300–773 K). This high thermoelectric performance is attributed to its ultra-low lattice thermal conductivity, caused by dense dislocations generated through heavy Te/S alloying and Cu interstitial doping. These dislocations in the lattice significantly enhance phonon scattering, minimizing lattice thermal conductivity while maintaining high carrier transport. Similarly, in GeTe thermoelectric materials,¹³⁰ dislocations and nano-domains enhance phonon scattering, thus reducing lattice thermal conductivity. Concurrently, this maintains carrier mobility and power factor, significantly improving the quality factor and maximizing thermoelectric performance. Masoumi and others²²² employed reshaped plastic deformation-induced dislocations to reduce lattice thermal conductivity in thermoelectric materials through mid-frequency phonon scattering and scattering at grain boundaries and point defects, thereby optimizing thermoelectric performance. Pan et al.²²³ enhanced the thermoelectric figure of merit by reducing lattice thermal conductivity through microstructure engineering. By employing a new melt centrifugation process to extrude excess eutectic liquid, microstructural modulation was achieved to manipulate dislocation formation and clean grain boundaries, forming a porous network with plate-like structures. In this manner, due to the combined effects of porosity, pore surface/junctions, grain boundaries, and lattice dislocations, phonon transport was significantly disrupted. These factors collectively led to a reduction in lattice thermal conductivity by about 60% compared to the regionally melted ingot, while charge carriers still moved relatively freely between the liquid-merged grains.

Additionally, other methods can effectively scatter phonons and reduce lattice thermal conductivity. For example, Yu et al.²²⁴ used quantum gaps, planar defects characterized by nanoscale potential wells, to selectively scatter phonons while effectively allowing carriers to pass through, decoupling carrier and phonon transporte shown in Fig. 28. The dispersed distribution of quantum gaps reduced lattice thermal conductivity, enabling the GeTe system to achieve a peak ZT of 2.6 and an average ZT of 1.6 (323–723 K) at 673 K. Yue and others²²⁵ studied the thermal transport and thermoelectric properties of the full Heusler compound Na₂TlSb using first-principles calculations combined with self-consistent phonon theory and the Boltzmann transport equation. The results showed that the strong quartic anharmonicity and temperature dependence of Tl atoms, as well as their jittery behavior, play a crucial role in the lattice stability of Na₂TlSb. The soft Tl–Sb bonding and the resonant bonding in the pseudo-cage formed by the interaction between Na and Sb atoms are the reasons for the extremely low lattice thermal conductivity.


	Fig. 28 Quantum gaps and their role in enhancing the performance of Ge–Bi–Te alloys. (a) The structural model of a quantum gap (QG) in the Ge–Bi–Te alloy. (b) Experimental quantum well and calculated quantum states in the QG region. (c) Schematic representation of the transport properties of QG, which allows carriers to freely pass through but strongly scatters phonons. (d) Peak ZTs and average ZTs (323–723 K) of representative high-performance lead-free GeTe thermoelectrics.²²⁴ Reproduced from ref. 224 with permission from Springer Nature, copyright (2022).

2.6 Unique structures

2.6.1 Texture. Texture refers to the orientation distribution of crystals within a material. In thermoelectric systems with significant anisotropy, particularly in layered systems, enhancing the degree of texturing often leads to a notable improvement in thermoelectric performance.²²⁷ Methods such as hot pressing, directional solidification, templating, and thermal calcination followed by secondary recrystallization are commonly considered principal approaches to achieve texture. Textured thermoelectric materials typically exhibit anisotropic electrical conductivity. Due to the uniformity in crystal orientation, the mobility of electrons or holes increases in specific directions, thereby enhancing electrical conductivity in those directions. At the same time, texturing also affects the Seebeck coefficient, as carrier transport is closely related to crystal orientation. Certain crystal orientations may enhance thermal conductivity, especially when crystals are aligned in directions with higher heat conduction. Beyond directly impacting thermoelectric performance, texture also improves the material's mechanical stability. Textured thermoelectric materials often possess better mechanical properties, which is crucial for the long-term stable operation of thermoelectric devices.

For example, in the study by Wang and others,²²⁸ it was found that as the degree of texturing increased, the ratio of in-plane to out-of-plane thermal and electrical conductivity also rose. However, regardless of the texturing level, the Seebeck coefficient remained almost isotropic. Wang and colleagues²²⁹ investigated the impact of thermally induced defects and texturing on the thermoelectric properties of FeSb₂ materials. They discovered that thermal deformation reduced thermal conductivity by enhancing phonon scattering and introduced weak anisotropy in resistivity and the Seebeck coefficient in the deformed samples. Research on Ge_1−xIn_xSb₂Te₄ single crystals by Chen et al.²³⁰ showed that texture significantly affects anisotropy, electrical conductivity, Seebeck coefficient, and thermal conductivity. Ge_0.93In_0.07Sb₂Te₄, aligned along the c-axis, exhibited a peak ZT_value 54% higher than the original GeSb₂Te₄. Bao and others²²⁶ synthesized Bi₂Te₃ nanostructures with controllable morphology using a solvothermal process and then produced bulk samples with controlled texture degree through spark plasma sintering (Fig. 29). The sintered Bi₂Te₃ nanostructured particles exhibited texture-dependent thermoelectric performance, with their Seebeck coefficient, electrical conductivity, and thermal conductivity optimized through appropriate texturing design. This ensures high carrier mobility and strong phonon scattering, achieving a peak ZT value of about 0.69 at 333 K.


	Fig. 29 Diagram of the sample's synthesis process, illustrating how texture affects the different transport behaviors of phonons and electrons.²²⁶ Reproduced from ref. 226 with permission from Elsevier, copyright (2020).

2.6.2 Single crystal. Single crystal structures refer to materials with continuous and uniform crystal arrangements, unlike the grain boundaries and heterogeneities found in polycrystalline materials. Single crystal structures lack grain boundaries or other defects, which in polycrystalline materials scatter charge carriers, reducing their mobility. Therefore, in single crystal materials, electrons and holes can move more freely, leading to increased electrical conductivity. Additionally, due to the anisotropic nature of carrier transport in single crystal structures, optimizing the crystal growth direction can further enhance the Seebeck coefficient. Furthermore, the anisotropy of single crystal materials can be used to further control thermal conductivity, minimizing heat conduction by choosing appropriate crystal growth directions. However, producing high-quality single crystal thermoelectric materials involves complex crystal growth techniques and expensive manufacturing costs. Given their excellent thermoelectric performance, single crystal thermoelectric materials hold great potential in high-performance thermoelectric applications.

For instance, Sanchela et al.²³¹ found that the single crystal structure of In₂Te₅ affects its thermoelectric performance. They observed lower thermal conductivity along the c-axis of the crystal compared to the direction perpendicular to the c-axis, while the Seebeck coefficient was higher along the c-axis. Additionally, the figure of merit (ZT) along the c-axis at room temperature was four times higher than that in the direction perpendicular to the c-axis.²³¹ Misra et al.²³² indicated that the single crystal structure of InTe significantly affects its thermoelectric properties, with notable anisotropy between the c-direction and the [110] direction of the crystal structure. The combination of low lattice thermal conductivity and relatively high power factor led to a maximum dimensionless thermoelectric figure of merit (ZT) of 0.61 along the [110] direction at 780 K. Jin et al. found²³³ that compared to the polycrystalline structure, the single crystal structure of Ag₈SnSe₆ had about 40% higher Hall mobility, though the lattice thermal conductivity was very similar. Zhao et al.²³⁴ showed that the single crystal structure of Cu_2−xSe did not significantly impact its thermoelectric performance; both single crystal and melt-quenched samples exhibited excellent thermoelectric properties with a figure of merit (ZT) as high as 1.7–1.8 at around 973 K. Li et al. proposed²³⁵ that the single crystal structure of Ag₉AlSe₆, with its complex crystal structure, weak bonding, and highly disordered cations, contributes to its ultra-low lattice thermal conductivity, making it a promising thermoelectric material with high figure of merit. Zhang et al. confirmed²³⁶ that the single crystal structure of Cu–S based compounds can influence their thermoelectric performance. They successfully fabricated Cu₆Fe₂S₈Sn₁ and Cu₁₆Fe_4.3S₂₄Sn₄Zn_1.7 as single-phase dense ceramics, with ZT values of 0.43 and 0.24 at 623 K, respectively. Zhao²³ reported unprecedented ZT values of 2.6 ± 0.3 in SnSe single crystals measured along the b-axis of the room-temperature orthorhombic cell at 923 K. This material also exhibited high ZT values of 2.36 ± 0.3 along the c-axis, but the ZT value significantly decreased to 0.8 ± 0.2 along the a-axis. They attributed the significantly high ZT value along the b-axis to the inherently ultra-low lattice thermal conductivity in SnSe, attributing the extremely low lattice thermal conductivity in SnSe (0.236 ± 0.03 W m⁻¹ K⁻¹ at 973 K) to anharmonicity as shown in Fig. 30.


	Fig. 30 ZT values along different axial directions; the uncertainty in ZT measurement is about 15% (error bars). Insets: on the left, a typical crystal; on the right, a crystal cleaved along the (100) plane, along with specimens cut along the three axes and their respective measurement directions. The inset diagram illustrates how crystals were cut for directional measurements; ZT values are indicated on blue, red, and grey arrows; the colors represent specimens oriented in different directions.²³ Reproduced from ref. 23 with permission from Springer Nature, copyright (2014).

2.6.3 Core–shell structures. Core-shell structures typically consist of a central core and one or more outer shell layers, each with distinct chemical or physical properties. In core–shell structures, selecting materials with high electrical conductivity for the core can provide efficient charge transport channels, while the shell layer can be designed with lower charge carrier density to reduce carrier scattering within the material, aiding in enhancing the overall material's electrical conductivity.⁷² The core–shell interface can act as a scattering center for phonons, effectively reducing lattice thermal conductivity. Additionally, interfaces between different materials may cause phonon localization, further suppressing thermal energy transfer. In terms of improving the chemical and thermal stability of thermoelectric materials, the shell layer can protect the core from environmental factors such as oxidation and corrosion, thereby extending the material's lifespan.

For example, Fu et al.²³⁷ conducted pioneering work in this direction by introducing a “core–shell” microstructure into Yb-filled skutterudite thermoelectric materials. The “core–shell” structure, formed by the thermal diffusion of nickel nanoparticles in Yb_0.2Co₄Sb₁₂ powder during hot pressing, consisted of ordinary “core” particles and nickel-rich nanoparticle “shells.” Due to increased carrier concentration and mobility, electrical resistivity was significantly reduced, and the sample with 0.2 weight percent nickel reached a maximum ZT of 1.07 at 723 K. Liu et al.²³⁸ found that added Cu₂Te always co-precipitates with Sb, forming an interesting Sb/CuTe core/shell structure; moreover, the interface between the core/shell precipitates and the PbTe matrix exhibited both coherent lattice and strong strain contrast, which is favorable for electron transport but unfavorable for phonon transport. Ultimately, a peak figure of merit ZT_max ≈ 1.6@823 K and an average ZT ≈ 1.0 (323–823 K) were achieved in the (PbTe)₈₁Sb₂Te₃–0.6Sb–2Cu₂Te sample, representing a good level for n-type PbTe-based thermoelectric materials. As shown in Fig. 31, Li et al.²³⁹ integrated β-Zn₄Sb₃ into the SnTe matrix to tune the thermoelectric properties of SnTe. A continuous in situ reaction occurred between the β-Zn₄Sb₃ additive and the SnTe matrix, forming a “core–shell” microstructure (Sb@ZnTe); at 873 K, an ultra-low lattice thermal conductivity was achieved, and ultimately, the SnTe-1.5% β-Zn₄Sb₃ sample reached a maximum ZT ≈ 1.32 at 873 K.


	Fig. 31 (a) The schematic diagram of the reaction process of the “core–shell” structure, (b and c) core–shell structure, electron probe microanalysis (EPMA). (d and e)Element analysis of SnTe-1.5% β-Zn₄Sb₃ samples.²³⁹ Reproduced from ref. 239 with permission from John Wiley and Sons, copyright (2020).

2.6.4 Porous structures. Porous structures are generally believed to reduce the thermal conductivity of thermoelectric materials, as air or other gases trapped in the pores are poor conductors of heat. Chen and colleagues²⁴⁰ designed and synthesized CaMnO₃ materials with nano, micro, and sub-millimeter scale cross-scale pores. As the pore size and porosity increased, the thermal conductivity sharply decreased. The extreme low lattice thermal conductivity was achieved due to multiple phonon scattering and boundary effects of sub-millimeter pores, highlighting the exceptional performance of porous materials in reducing lattice thermal conductivity. Li and others,²⁴¹ using a unique BiI₃ sublimation technique, introduced a porous network into the tetrahedrite Cu₁₂Sb₄S₁₃ base material. Eventually, the addition of a small amount of BiI₃ (0.7 volume%) led to about a 72% reduction in lattice thermal conductivity, and due to an unexpected enhancement in carrier mobility, the electrical conductivity was improved. As a result, an enhanced ZT value of 1.15 was obtained in porous tetrahedrite at 723 K, as shown in Fig. 32.


	Fig. 32 (a) Schematic of porous network formation during BiI₃ sublimation. (b and c) SEM images of fracture surfaces of AD 0 vol% (b) and AP 0.7 vol%. (c) Samples showing 3D porous structures. (d and e) Temperature dependence of total thermal conductivity κ (d) and lattice thermal conductivity κ_L (e). (f) Experimental and EMT-corrected lattice thermal conductivity of porous AP 0.7 vol%, the Debye–Callaway model predicts EMT-corrected κ_L, considering Umklapp process (U), porous interfaces (I), precipitates (P), point defects (PD), dislocation cores (DC), and strains (DS, D = DC + DS). (g) Frequency-dependent accumulative reduction in EMT-corrected lattice thermal conductivity of porous AP 0.7 vol% due to various scattering mechanisms.²⁴¹ Reproduced from ref. 241 with permission from John Wiley and Sons, copyright (2021).

2.6.5 Symmetry manipulation. Symmetry manipulation in thermoelectric materials involves altering the material's symmetry properties to directly influence the Seebeck coefficient, electrical conductivity, and lattice thermal conductivity, thereby optimizing thermoelectric performance. One advantage of high-symmetry thermoelectric materials is their very high band degeneracy, while the advantage of low-symmetry thermoelectric materials lies in their very low lattice thermal conductivity due to strong anharmonicity. If the symmetry disruption of band degeneracy is minimal, these two advantages may be simultaneously realized.³¹

By reducing the symmetry of a material, band edge splitting or band flattening can be achieved, thereby increasing the effective mass of the carriers. As indicated by eqn (20), the effective mass m* is related to the inverse of the band curvature; the flatter the band, the higher the carrier effective mass m*, which in turn enhances the Seebeck coefficient and increases the power factor.


	(20)

Here, m* represents the effective mass of the electron, ℏ is the reduced Planck constant, E is the electron energy, and k is the crystal momentum (wave vector), where

determines the curvature of the band.

The reduction of lattice thermal conductivity is also crucial for enhancing the performance of thermoelectric materials. Symmetry manipulation, through the introduction of lattice distortions, creation of micro defects, or design of asymmetric nanostructures, can effectively increase phonon scattering mechanisms, thereby reducing lattice thermal conductivity. Additionally, local stress fields generated by symmetry breaking can affect phonon propagation paths, and asymmetry can cause asymmetric or hierarchical chemical bonding and high anharmonicity, further reducing thermal conductivity.^{20,23,74,186,242} Classical methods for controlling material symmetry generally involve phase transitions,^{29,31,59,66,243} such as the work by Li and his team,²⁴⁴ which found that alloying MnCdTe₂ in GeSe crystals enhanced symmetry to form a high concentration of Ge vacancies, as shown in Fig. 33, and produced high electrical conductivity with metallic-like conductive behavior. Additionally, rhombohedral Ge_1−yBi_ySe(MnCdTe₂)_x exhibits high valley degeneracy and small effective band mass, providing good Seebeck coefficients and high carrier mobility.


	Fig. 33 A schematic diagram shows the increased cationic vacancies in GeSe by enhancing crystal symmetry upon.²⁴⁴ Reproduced from ref. 244 with permission from Elsevier, copyright (2022).

Research by Hu et al.²⁴⁵ also shows that high crystal symmetry and the presence of nanoscale defects are beneficial for thermoelectric performance. High-symmetry crystals with suitable electronic structures tend to provide multiple carrier channels, thereby enhancing electrical conductivity without sacrificing the Seebeck coefficient. For instance, doping with Mg or Ga transformed monoclinic Cu₂SnSe₃ into a cubic structure, this symmetry elevation increased the effective mass from 0.8m_e to 2.6m_e (m_e refers to the mass of a free electron), and the power factor from 4.3 μW cm⁻¹ K⁻² in Cu₂SnSe₃ to 11.6 μW cm⁻¹ K⁻². Guo and his research team²⁴⁶ transformed hexagonal Ge₄Se₃Te into rhombohedral phase by Te alloying, which exhibited higher valley degeneracy than hexagonal Ge₄Se₃Te, induced strong band convergence and band inversion effects, significantly enhancing the Seebeck coefficient and power factor.

3 Outlook and challenge

3.1 Synergistic effect

In the optimization process of thermoelectric material performance, it is not through a single strategy that the thermoelectric properties are modulated, but rather a combination of various methods and strategies for synergistic optimization. For instance, in the research by Zhu²⁴⁷ et al., to achieve an overall enhancement of GeTe across a wide temperature range, they utilized a functionally separated electronic band engineering strategy (resonant levels and band convergence) combined with the construction of high-density defects by designing multi-element SnSe–In–Sb co-doping. They found that SnSe alloying primarily promoted band convergence in GeTe at high temperatures, indium doping could create resonant levels to enhance thermoelectric (TE) performance near room temperature, and antimony optimized symmetry and overall carrier concentration, thereby jointly increasing effective mass and the Seebeck coefficient. Additionally, the construction of various phonon scattering centers, including high-density Ge micro/nano-precipitates, van der Waals gaps, dislocations, and strong stress fields, significantly suppressed phonon transport. Benefitting from these synergistic effects, a peak ZT of about 2.0 at 653 K and an average ZT of about 1.2 over the range of 303 to 803 K were achieved in the samples.

In the practical optimization of thermoelectric materials, synergistic effects not only simply add up the effects of each component but can produce a composite impact that exceeds the sum of individual component effects^248–251, as shown in Fig. 34. In the design of thermoelectric materials, the interplay between electrical conductivity, thermal conductivity, and the Seebeck coefficient is a classic example of synergistic effect. The key to optimizing thermoelectric materials lies in decoupling and balancing these parameters to achieve the best thermoelectric conversion efficiency.


	Fig. 34 Diagram of synergistic effects enhancing thermoelectric performance: band engineering strategies (resonance energy levels and band convergence), creating high-density defects, including Ge micro/nano precipitates, van der Waals gaps, dislocations, and strong stress fields as phonon scattering centers, greatly inhibit phonon transmission.²⁴⁷ Reproduced from ref. 247 with permission from Elsevier, copyright (2024).

3.2 Materials genome and machine learning

The future development of thermoelectric materials will rely on the integration of multiple disciplines such as physics, chemistry, materials science, and nanotechnology. The advancement of artificial intelligence has brought numerous opportunities to the field of materials, enabling multidisciplinary collaboration to deepen our understanding of the fundamental principles of thermoelectric effects and to drive the development of new materials and structures. The concept of the materials genome integrates computational materials science, high-throughput experimental techniques, and digital data processing to predict the performance of novel thermoelectric materials, such as band structures, carrier concentrations, and thermoelectric figures of merit, through computational simulations and machine learning algorithms. This reduces dependence on traditional trial-and-error methods, significantly accelerating research progress.

Since the initiation of the “Materials Genome Initiative,” multiple material databases have been established, significantly advancing many fields of materials science. Chen et al.²⁵² introduced the Materials Informatics Platform with 3D structural information (MIP-3d), as shown in Fig. 35(a) and (b). MIP-3d includes over 80 [thin space (1/6-em)] 000 structural entries, primarily sourced from the inorganic crystal structure database. The platform has conducted density functional theory calculations on over 30000 entries, covering relaxed crystal structures, density of states, and band structures. Additionally, calculations of equations of state and sound velocities have been performed on over 12 [thin space (1/6-em)] 000 entries. Notably, for entries with band gap values exceeding 0.3 electron volts, we analyzed band degeneracy at the valence band maximum and conduction band minimum. The electrical transport properties of approximately 4400 entries have also been calculated and are displayed in MIP-3d using a constant electron–phonon coupling approximation. These calculations of band degeneracy and electrical transport properties make MIP-3d a database specifically designed for thermoelectric applications. Jin²⁵³ devised a high-throughput method to compute deformation potential energies of semiconductors in the MatHub-3d database, as shown in Fig. 35(c). The deformation potential energy of 11 [thin space (1/6-em)] 993 materials was calculated, resulting in 9957 compounds with convergent electrical transport characteristics. The method identified 332 promising p-type and 321 n-type thermoelectric materials. A total of 156 compounds were screened for potential good n-type and p-type thermoelectric transport characteristics. Several typical compounds' band structures and chemical bonding information were showcased to highlight band and bonding characteristics favorable for the thermoelectric effect. Yao et al.²⁵⁴ established their own materials data repository, MIP-3d, and used in-house software such as TransOpt for calculations. To date, it has cataloged over 30 [thin space (1/6-em)] 000 electronic structures, 4400 electrical transport properties, and 12000 state equations and sound speed data, which are critical criteria for finding high-quality thermoelectric materials. The computational methods of MIP-3d primarily include two modules: initial structure inspection and high-throughput computation (HTP), as depicted in Fig. 35(d).


	Fig. 35 (a) Computational workflow for the dataset of 48770 compounds in the MIP-3d platform.²⁵² (b) Violin plot showing the distribution of maximum power factors calculated under the fixed relaxation time approximation in the MP database, separated by anion type. The red line indicates the median calculated power factors for different anions.²⁵² Reproduced from ref. 252 with permission from Royal Society of Chemistry, copyright (2016). (c) Workflow of high-throughput calculations.²⁵³ Reproduced from ref. 253 with permission from Springer Nature, copyright (2023). (d) Computational method flowchart of MIP-3d.²⁵⁴ Reproduced from ref. 254 with permission from Springer Nature, copyright (2021). (e) Overall workflow for generating datasets and training the elemental-SDNNFF model to predict phononic properties.²⁵⁵ Reproduced from ref. 255 with permission from Springer Nature, copyright (2023).

Liu et al.²⁵⁶ used entropy as a performance metric similar to a global gene, demonstrating how high-throughput screening methods can design high-entropy multicomponent thermoelectric materials. Optimizing entropy as an effective guide can significantly enhance thermoelectric performance, not only by reducing lattice thermal conductivity to theoretical minimum values but also by enhancing crystal structure symmetry to achieve higher Seebeck coefficients.

Simultaneously, neural network-based machine learning has also emerged in the field of thermoelectric materials,^257–259 with Fig. 35(e) illustrating the workflow for training the elemental-SDNNFF model to predict phononic properties.²⁵⁵ Applying the elemental-SDNNFF model allows for efficient and accurate prediction of phononic properties for a large array of materials. This work primarily targeted 77 [thin space (1/6-em)] 091 cubic crystal structures, encompassing 63 chemical elements and 16 structural prototypes. The model was initially trained on 3107 structures and continuously improved through active learning methods, ultimately capable of predicting complete phononic properties of stable structures three orders of magnitude faster than DFT (Density Functional Theory).

3.3 Challenges

One of the primary goals in enhancing the performance of thermoelectric materials is to increase their figure of merit (ZT). Efforts to decouple various thermoelectric parameters through diverse strategies to improve the ZT value have been a consistent direction of research for thermoelectric scholars.^260–263 However, these strategies face numerous challenges in practical applications. Low-dimensional strategies, due to their unique quantum effects, can achieve high thermoelectric figures of merit, but the anisotropy of low-dimensional materials leads to significant measurement errors in practical assessments. When optimizing thermoelectric performance using point defects, the systems available for utilization are relatively limited. Most thermoelectric materials improve their performance through doping, yet maintaining the original designed stoichiometry often presents challenges. Nano-composite strategies, which decouple electron and phonon transport by introducing nanoparticles and secondary phases, tend to be costly. Band engineering has made significant progress through the robust development of modern solid-state physics and quantum mechanics, but entering the new century, with limitations due to breakthroughs in innovative physical theories, a broad array of thermoelectric researchers are actively seeking new theoretical guidance. Structural control has always been a focal point in materials science research. From single-crystal to polycrystalline materials, from core–shell to porous structures, designing unique structures to address existing problems in thermoelectric materials is a promising strategy. However, the slow growth of single crystals and the special fabrication processes required for porous structures, which may compromise the mechanical properties of the materials, are challenges. Fortunately, more imaginative and futuristic fabrication techniques could potentially be applied to the preparation of thermoelectric materials. With the rapid development of space technology, the microgravity environment of space factories could influence the growth modes of material crystals, making it easier to produce foam baths and highly uniform porous materials. These novel technologies could offer new solutions to a wide range of materials science challenges, including thermoelectric materials.

In addition to the challenges in designing and fabricating thermoelectric materials mentioned above, thermoelectric materials also face many problems in practical applications, with some of the main challenges as follows:

3.3.1 High-temperature stability and reliability. Thermoelectric materials often need to operate in high-temperature environments for extended periods in practical applications, demanding high thermal and mechanical stability. Thermal cycling, oxidation, and other high-temperature degradation mechanisms can significantly reduce the performance of thermoelectric materials. One important use of thermoelectric materials is to provide electrical power support for deep-space exploration on RTGs, such as the highly popular Cu₂Se thermoelectric material, which has been developed by 3M Corporation, Jet Propulsion Laboratory, etc., for the 1982 Jupiter Orbiter mission.^264–266 However, significant copper deposition at the cold end of the Cu_1.97Ag_0.03Se leg(as shown in Fig. 36(a)–(c)²⁶⁶) led to selenium evaporation at the hot end and increased contact resistance between the material and electrodes, severely reducing the module's performance and stability, and even completely destroying the TE module,^270,271 thus forcing related funding to be halted. Another typical example in terms of stability is the AgSbTe₂ material, which is highly promising for medium-temperature ranges (400–700 K).²⁷² However, the original AgSbTe₂ is unstable and decomposes into Sb₂Te₃ and Ag₂Te below 633 K,^273,274 with Ag₂Te precipitating a phase change at about 418 K. The presence of n-type Ag₂Te not only makes p-type AgSbTe₂ unstable when heated but also reduces its thermoelectric performance.^273,274 Similarly, the thermal stability of Mg₃Sb₂-based thermoelectric materials in the mid-temperature region leaves much to be desired,^275,276 as magnesium's high vapor pressure and reactivity at elevated temperatures lead to significant losses and decomposition.²⁷⁷ This causes high-density Mg vacancies and the formation of a secondary Bi phase in the Mg₃(Sb, Bi)₂ alloy, which severely degrades the material's performance and may cause a switch from n-type to p-type conductivity.²⁷⁶ Therefore, ensuring the high-temperature stability of thermoelectric materials is crucial for their widespread application in energy conversion.


	Fig. 36 (a) Sample after 24 hours of current application. (b) Optical microscopy shows copper deposition on the current-sink face. (c) SEM image of the top surface with copper nanowire bundles (“whiskers”) formed by electromigration.²⁶⁶ Reproduced from ref. 266 with permission from Springer Nature, copyright (2013). (d) Schematic diagram of the synthesis process of the composite. (e) Large-scale fabricated composite thin films.²⁶⁷ Reproduced from ref. 267 with permission from American Chemical Society, copyright (2022). (f) Fabrication process of the composite films and schematic diagram of the OTE device. (g) Degradation characteristics of the transient OTE device in pure acetone at room temperature.²⁶⁸ Reproduced from ref. 268 with permission from American Chemical Society, copyright (2023). (h) Daytime schematic of water production and power generation through solar radiative heating. (i) Nighttime schematic of water vapor capture from air and power generation through radiative cooling from the universe. (j) Photograph of water condensation during the water collection stage.²⁶⁹ Reproduced from ref. 269 with permission from Springer Nature, copyright (2022).

3.3.2 Manufacturing techniques and scale-up production: challenges and opportunities. Scaling up the synthesis of thermoelectric materials from laboratory scale to industrial scale production presents a challenging process.^278,279 This involves not only technical difficulties but also economic considerations. Achieving scale-up production is key to developing scalable synthesis methods while maintaining material performance consistency and reliability.^280–282 This typically requires process optimization and the development of new equipment, as well as ongoing technological innovation aimed at reducing production costs and enhancing production efficiency. As shown in Fig. 36(d) and (e),²⁶⁷ an ultra-large 25 × 20 cm² commercial graphite composite film was prepared using a typical industrial hot pressing method, with a cost of only 7250 μW g per m per K² per $¹ for (S²σ/cos [thin space (1/6-em)]

t). The entire preparation process is very short, taking only 10 minutes per cycle, demonstrating a beneficial attempt in the mass production of thermoelectric materials. Moreover, scale-up production also requires effective integration with market demand and supply chain management to ensure the economic feasibility and market competitiveness of the production process.

3.3.3 Cost-effectiveness and environmental impact: balancing sustainability. While certain semiconductor materials like Bi₂Te₃ (ref. 283–285) and PbTe^{25,51,286,287} exhibit excellent thermoelectric performance, their widespread use is significantly restricted mainly because these materials rely on rare or harmful elements such as tellurium and lead. The extraction and use of these elements not only incur high costs but may also cause lasting environmental damage, thus conflicting with sustainability development goals. Therefore, researchers and developers must weigh the environmental impact and economic benefits when selecting materials, exploring more environmentally friendly and cost-effective alternatives,^148,288 to promote the sustainable development of thermoelectric technology. Some interesting attempts have been made in the field of organic degradable thermoelectric materials.^289–293 For example, J. Kwak et al.²⁶⁸ achieved a high thermoelectric power factor of 51.8 μW m⁻¹ K⁻² by incorporating vitamin C (VC) as an additive in high-performance organic thermoelectric (OTE) devices based on poly(3,4-ethylenedioxythiophene) (styrenesulfonate) (PEDOT). Moreover, these devices can be completely degraded by naturally occurring substances, as shown in Fig. 36(f) and (g), demonstrating significant environmental advantages.

3.3.4 Integration and application complexity: design and system integration. Designing high-performance thermoelectric systems requires not only the use of efficient thermoelectric materials but also the optimization of thermoelectric module designs, including interface engineering and thermal management. Furthermore, effective integration of thermoelectric systems with other energy systems (such as solar energy and waste heat recovery systems) is key to enhancing overall energy efficiency.^294–296 This requires designers to possess interdisciplinary knowledge and skills to achieve the best performance and energy efficiency of the systems. An interesting example, as shown in Fig. 36(h)–(j),²⁶⁹ is demonstrated by Li et al. They presented a hybrid device that simultaneously achieves solar-assisted water harvesting (SAWH) and 24 hours thermoelectric power generation (TEPG), enabling the combined production of water and electricity. During the day, solar energy drives the hybrid device to produce atmospheric water and generate thermoelectric power, as illustrated in Fig. 36(h). At night, the device captures water vapor from the air and generates electricity through radiative cooling to the cosmos, as shown in Fig. 36(i). This efficient system integration results in high-efficiency water production and 24 hours power generation, as depicted in Fig. 36(j). It is evident that effective system integration not only enhances the performance of thermoelectric systems but also promotes the use of thermoelectric technology in various application scenarios, including but not limited to automotive, industrial, and civilian facilities,^297–300 thereby achieving efficient energy utilization and sustainable environmental development.

4 Conclusion

This review paper comprehensively introduces various optimization methods for thermoelectric materials, a promising class of energy conversion materials. It discusses in detail how low dimensionality and quantum confinement effects significantly enhance the performance of thermoelectric materials. Through case studies of two-dimensional, one-dimensional, and zero-dimensional materials, we observed the profound impacts of size effects and quantum confinement on carrier and phonon transport properties. Point defect engineering, as an effective means to adjust the electronic and thermal transport properties of thermoelectric materials, demonstrates the potential of achieving optimized performance through microstructural control. Additionally, the study of nano-composite materials highlights strategies for increasing interface scattering and reducing thermal conductivity, thereby enhancing the thermoelectric efficiency of the materials.

Band engineering is another strategy that manipulates the micro-electronic structure to enhance thermoelectric performance. By optimizing carrier effective mass, utilizing resonant states, achieving band degeneracy and convergence, and adjusting the band structure, band engineering offers multiple possibilities for designing high-performance thermoelectric materials. This fine control of band structures not only optimizes carrier transport properties but also aids in achieving higher Seebeck coefficients and electrical conductivity while reducing thermal conductivity.

In terms of microstructural control, this paper discusses the thermoelectric performance of textured, single-crystal, core–shell, and porous structures. These special structures demonstrate potential in reducing thermal conductivity and optimizing carrier transport through symmetry control and structural customization. Moreover, the application of phonon engineering plays a significant role in achieving low thermal conductivity and high thermoelectric conversion efficiency, proving that precise control of phonon scattering mechanisms can effectively enhance the overall performance of materials.

Looking forward, synergistic effects through a comprehensive application of low-dimensional effects, point defect engineering, nano-composite materials, and band engineering can maximize the performance of thermoelectric materials. This multi-strategy integrated optimization approach not only enhances individual performance metrics but also optimizes performance on a holistic level.

Material genomics and machine learning exhibit tremendous potential in the research of thermoelectric materials. The application of these advanced technologies will greatly accelerate the discovery and optimization process of new thermoelectric materials, using data-driven approaches to predict material performance and guide experimental design. This not only saves research and development time and costs but may also reveal previously unknown material behaviors and optimization pathways.

Beyond the inherent challenges of optimization strategies, thermoelectric materials also face issues with high-temperature stability and reliability in practical applications. Additionally, the cost-effectiveness and environmental impact of these materials are important considerations, necessitating the development of more economical and environmentally friendly alternative materials. Also, scaling up laboratory-scale synthesis to industrial production while maintaining performance consistency is a key challenge, requiring technological innovation and optimized production processes. Finally, optimizing the design of thermoelectric modules and their effective integration with other energy systems is crucial for enhancing the overall energy efficiency of thermoelectric materials.

In summary, through a series of detailed discussions and analyses, we provide deep scientific insights and practical guidance for the research and application of thermoelectric materials. These studies not only enrich our understanding of the science of thermoelectric materials but also drive technological advancement and innovation in this field. Moving forward, as new technologies and materials continue to develop, research and applications of thermoelectric materials will progress towards higher efficiency and broader application areas, offering more possibilities for energy conversion and utilization.

Abbreviations

SPB	Single Parabolic Band model
SWCNT	Single-Walled Carbon Nanotubes
NWs	Nanowires
COP	Coefficient of Performance
CQD	Colloidal Quantum Dots
DFT	Density Functional Theory
CVD	Chemical Vapor Deposition
PVD	Physical Vapor Deposition
CBM	Conduction Band Minima
QG	Quantum Gap
EF	Fermi Energy
MP	Materials Project
MIP-3d	Materials Informatics Platform with 3D structural information
HTP	High-Throughput Computation
SAWH	Solar-assisted Water Harvesting
TEPG	Thermoelectric Power Generation

Data availability

The datas presented in this review come from the corresponding references.

Author contributions

Conceptualization: Haiwei Han, Lihua Yu, Junhua Xu; methodology: Haiwei Han, Xingmen Wu, Yaohong Jiang, Tao Li; software: Haiwei Han, Bin Zuo, Shunuo Bian; validation: Haiwei Han, Lijun Zhao, Bin Zuo, Yaohong Jiang; formal analysis: Haiwei Han, Bin Zuo, Shunuo Bian; investigation: Lijun Zhao, Tao Li, Xinyue Liu; data curation: Haiwei Han, Yaohong Jiang; writing – original draft: Haiwei Han, Lijun Zhao, Jiali Bi; visualization: Xingmen Wu, Chunyan Chen; writing – review & editing: Haiwei Han; resources, supervision: Lijun Zhao, Junhua Xu, Lihua Yu; project administration: Junhua Xu, Lihua Yu, Lijun Zhao; funding acquisition: Junhua Xu, Lihua Yu, Lijun Zhao.

Conflicts of interest

The authors declare no conflict of interest and all authors have read and agreed to the published version of the manuscript.

Acknowledgements

This research was funded by “National Natural Science Foundation of China” [No. 52071159 and 52172090], and The University-Industry Research Cooperation Project [BY20221151].

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